220101 Pure Mathematics
6Mathematics
4Lie group
4Pro-Lie groups
3Abelian topological group
3Exponential function
3Free topological vector space
3Projective limit
20199 Other Mathematical Sciences
20802 Computation Theory and Mathematics
2Compact groups
2Coproducts
2Embedding
2Free abelian topological group
2Free locally convex space
2Free topological group
2Lie algebra
2Locally compact group
2Open mapping theorem
2Pro-Lie Groups

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A novel approach for predicting trading signals of a stock market index

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2010**Type:**Text , Book chapter**Relation:**Forecasting models: Methods and applications p. 145-160**Full Text:**false**Reviewed:**

A topological group observation on the Banach-Mazur separable quotient problem

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2019**Type:**Text , Journal article**Relation:**Topology and Its Applications Vol. 259, no. (2019), p. 283-286**Full Text:****Reviewed:****Description:**The Separable Quotient Problem of Banach and Mazur asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space. It has remained unsolved for 85 years but has been answered in the affirmative for special cases such as reflexive Banach spaces. An affirmative answer to the Separable Quotient Problem would obviously imply that every infinite-dimensional Banach space has a quotient topological group which is separable, metrizable, and infinite-dimensional in the sense of topology. In this paper it is proved that every infinite-dimensional Banach space has as a quotient group the separable metrizable infinite-dimensional topological group, T

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2019**Type:**Text , Journal article**Relation:**Topology and Its Applications Vol. 259, no. (2019), p. 283-286**Full Text:****Reviewed:****Description:**The Separable Quotient Problem of Banach and Mazur asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space. It has remained unsolved for 85 years but has been answered in the affirmative for special cases such as reflexive Banach spaces. An affirmative answer to the Separable Quotient Problem would obviously imply that every infinite-dimensional Banach space has a quotient topological group which is separable, metrizable, and infinite-dimensional in the sense of topology. In this paper it is proved that every infinite-dimensional Banach space has as a quotient group the separable metrizable infinite-dimensional topological group, T

An open mapping theorem

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2016**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 94, no. 1 (2016), p. 65-69**Full Text:****Reviewed:****Description:**It is proved that any surjective morphism f : Z(k) -> K onto a locally compact group K is open for every cardinal k. This answers a question posed by Hofmann and the second author.

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2016**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 94, no. 1 (2016), p. 65-69**Full Text:****Reviewed:****Description:**It is proved that any surjective morphism f : Z(k) -> K onto a locally compact group K is open for every cardinal k. This answers a question posed by Hofmann and the second author.

An open mapping theorem for pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Journal article**Relation:**Journal of the Australian Mathematical Society Vol. 83, no. 1 (2007), p. 55-77**Full Text:**false**Reviewed:****Description:**A pro-Lie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected pro-Lie groups is open. In fact this remains true for almost connected pro-Lie groups where a topological group is called almost connected if the factor group modulo the identity component is compact. As consequences we get a Closed Graph Theorem and the validity of the Second Isomorphism Theorem for pro-Lie groups in the almost connected context. © 2007 Australian Mathematical Society.**Description:**C1**Description:**2003005492

Cardinalities of locally compact groups and their Stone-Čech compactifications

- Itzkowitz, Gerald, Morris, Sidney, Tkachuk, Vladimir

**Authors:**Itzkowitz, Gerald , Morris, Sidney , Tkachuk, Vladimir**Date:**2003**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 67, no. 3 (2003), p. 353-364**Full Text:**false**Reviewed:****Description:**If G is any Hausdorff topological group and**Description:**C1**Description:**2003000377

Compact homeomorphism groups are profinite

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Type:**Text , Journal article**Relation:**Topology and its Applications Vol. , no. (), p.**Full Text:**false**Reviewed:****Description:**If the homeomorphism group H (X) of a Tychonoff space X is compact in the compact open topology, then it is a profinite topological group. © 2012.

Contributions to the structure theory of connected pro-Lie groups

- Morris, Sidney, Hofmann, Karl

**Authors:**Morris, Sidney , Hofmann, Karl**Date:**2009**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 33, no. (2009), p. 225-237**Full Text:**false**Description:**We present some recent results in the structure theory of pro-Lie groups and locally compact groups, improvements of known results, and open problems.

Density character of subgroups of topological groups

- Leiderman, Arkady, Morris, Sidney, Tkachenko, Mikhail

**Authors:**Leiderman, Arkady , Morris, Sidney , Tkachenko, Mikhail**Date:**2017**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 369, no. 8 (2017), p. 5645-5664**Full Text:****Reviewed:****Description:**We give a complete characterization of subgroups of separable topological groups. Then we show that the following conditions are equivalent for an omega-narrow topological group G: (i) G is homeomorphic to a subspace of a separable regular space; (ii) G is topologically isomorphic to a subgroup of a separable topological group; (iii) G is topologically isomorphic to a closed subgroup of a separable path-connected, locally path-connected topological group. A pro-Lie group is a projective limit of finite-dimensional Lie groups. We prove here that an almost connected pro-Lie group is separable if and only if its weight is not greater than the cardinality c of the continuum. It is deduced from this that an almost connected pro-Lie group is separable if and only if it is homeomorphic to a subspace of a separable Hausdorff space. It is also proved that a locally compact (even feathered) topological group G which is a subgroup of a separable Hausdorff topological group is separable, but the conclusion is false if it is assumed only that G is homeomorphic to a subspace of a separable Tychonoff space. We show that every precompact (abelian) topological group of weight less than or equal to c is topologically isomorphic to a closed subgroup of a separable pseudocompact (abelian) group of weight c. This result implies that there is a wealth of closed non-separable subgroups of separable pseudocompact groups. An example is also presented under the Continuum Hypothesis of a separable countably compact abelian group which contains a non-separable closed subgroup.

**Authors:**Leiderman, Arkady , Morris, Sidney , Tkachenko, Mikhail**Date:**2017**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 369, no. 8 (2017), p. 5645-5664**Full Text:****Reviewed:****Description:**We give a complete characterization of subgroups of separable topological groups. Then we show that the following conditions are equivalent for an omega-narrow topological group G: (i) G is homeomorphic to a subspace of a separable regular space; (ii) G is topologically isomorphic to a subgroup of a separable topological group; (iii) G is topologically isomorphic to a closed subgroup of a separable path-connected, locally path-connected topological group. A pro-Lie group is a projective limit of finite-dimensional Lie groups. We prove here that an almost connected pro-Lie group is separable if and only if its weight is not greater than the cardinality c of the continuum. It is deduced from this that an almost connected pro-Lie group is separable if and only if it is homeomorphic to a subspace of a separable Hausdorff space. It is also proved that a locally compact (even feathered) topological group G which is a subgroup of a separable Hausdorff topological group is separable, but the conclusion is false if it is assumed only that G is homeomorphic to a subspace of a separable Tychonoff space. We show that every precompact (abelian) topological group of weight less than or equal to c is topologically isomorphic to a closed subgroup of a separable pseudocompact (abelian) group of weight c. This result implies that there is a wealth of closed non-separable subgroups of separable pseudocompact groups. An example is also presented under the Continuum Hypothesis of a separable countably compact abelian group which contains a non-separable closed subgroup.

Editors' cut : Managing scholarly journals in mathematics and IT

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Research and Practice in Information Technology Vol. 37, no. 4 (2005), p. 299-309**Full Text:**false**Reviewed:****Description:**The first version of this essay was jointly delivered by the authors as a colloquium lecture at the University of Ballarat on 24 November, 2004. A second, expanded and illustrated version was published in German in the Mitteilungen der Deutschen Mathematikervereinigung early in 2005. Because of the very positive feedback, the authors decided it would be useful to publish a version in English in a computing journal. The purpose of the essay is to provide advice and information to authors of articles about publishing in scholarly journals from an editor's perspective. Of particular importance are remarks about etiquette.**Description:**C1

Effectiveness of using quantified intermarket influence for predicting trading signals of stock markets

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at Data Mining and Analytics 2007: Sixth Australasian Data Mining Conference, AusDM 2007 Vol. 70, p. 171-179**Full Text:****Reviewed:**

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at Data Mining and Analytics 2007: Sixth Australasian Data Mining Conference, AusDM 2007 Vol. 70, p. 171-179**Full Text:****Reviewed:**

Embedding into free topological vector spaces on compact metrizable spaces

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2018**Type:**Text , Journal article**Relation:**Topology and its Applications Vol. 233, no. (2018), p. 33-43**Full Text:**false**Reviewed:****Description:**For a Tychonoff space X, let V(X) be the free topological vector space over X. Denote by I, G, Q and Sk the closed unit interval, the Cantor space, the Hilbert cube Q=IN and the k-dimensional unit sphere for k

Embedding of the free abelian topological group A (X ⊕ X) into A (X)

- Krupski, Mikolaj, Leiderman, Arkady, Morris, Sidney

**Authors:**Krupski, Mikolaj , Leiderman, Arkady , Morris, Sidney**Date:**2019**Type:**Text , Journal article**Relation:**Mathematika Vol. 65, no. 3 (2019), p. 708-718**Full Text:**false**Reviewed:****Description:**We consider the following question: for which metrizable separable spaces X does the free abelian topological group A (X ⊕ X) isomorphically embed into A (X). While for many natural spaces X such an embedding exists, our main result shows that if X is a Cook continuum or X is a rigid Bernstein set, then A(X ⊕ X) does not embed into A(X) as a topological subgroup. The analogous statement is true for the free boolean group B (X).**Description:**We consider the following question: for which metrizable separable spaces X does the free abelian topological group A (X

Free subspaces of free locally convex spaces

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2018**Type:**Text , Journal article**Relation:**Journal of Function Spaces Vol. 2018, no. (2018), p. 1-5**Full Text:****Reviewed:****Description:**Abstract If X and Y are Tychonoff spaces, let and be the free locally convex space over and , respectively. For general and , the question of whether can be embedded as a topological vector subspace of is difficult. The best results in the literature are that if can be embedded as a topological vector subspace of , where , then is a countable-dimensional compact metrizable space. Further, if is a finite-dimensional compact metrizable space, then can be embedded as a topological vector subspace of . In this paper, it is proved that can be embedded in as a topological vector subspace if is a disjoint union of a countable number of finite-dimensional locally compact separable metrizable spaces. This is the case if It is also shown that if and denote the Cantor space and the Hilbert cube , respectively, then (i) is embedded in if and only if is a zero-dimensional metrizable compact space; (ii) is embedded in if and only if is a metrizable compact space.**Description:**If

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2018**Type:**Text , Journal article**Relation:**Journal of Function Spaces Vol. 2018, no. (2018), p. 1-5**Full Text:****Reviewed:****Description:**Abstract If X and Y are Tychonoff spaces, let and be the free locally convex space over and , respectively. For general and , the question of whether can be embedded as a topological vector subspace of is difficult. The best results in the literature are that if can be embedded as a topological vector subspace of , where , then is a countable-dimensional compact metrizable space. Further, if is a finite-dimensional compact metrizable space, then can be embedded as a topological vector subspace of . In this paper, it is proved that can be embedded in as a topological vector subspace if is a disjoint union of a countable number of finite-dimensional locally compact separable metrizable spaces. This is the case if It is also shown that if and denote the Cantor space and the Hilbert cube , respectively, then (i) is embedded in if and only if is a zero-dimensional metrizable compact space; (ii) is embedded in if and only if is a metrizable compact space.**Description:**If

Free topological vector spaces

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2017**Type:**Text , Journal article**Relation:**Topology and its Applications Vol. 223, no. (2017), p. 30-49**Full Text:**false**Reviewed:****Description:**In this paper the free topological vector space V(X) over a Tychonoff space X is defined and studied. It is proved that V(X) is a kω-space if and only if X is a kω-space. If X is infinite, then V(X) contains a closed vector subspace which is topologically isomorphic to V(N). It is proved that for X a k-space, the free topological vector space V(X) is locally convex if and only if X is discrete and countable. The free topological vector space V(X) is shown to be metrizable if and only if X is finite if and only if V(X) is locally compact. Further, V(X) is a cosmic space if and only if X is a cosmic space if and only if the free locally convex space L(X) on X is a cosmic space. If a sequential (for example, metrizable) space Y is such that the free locally convex space L(Y) embeds as a subspace of V(X), then Y is a discrete space. It is proved that V(X) is a barreled topological vector space if and only if X is discrete. This result is applied to free locally convex spaces L(X) over a Tychonoff space X by showing that: (1) L(X) is quasibarreled if and only if L(X) is barreled if and only if X is discrete, and (2) L(X) is a Baire space if and only if X is finite. © 2017 Elsevier B.V.

Identifying and distinguishing various varieties of abelian topological groups

- McPhail, Carolyn, Morris, Sidney

**Authors:**McPhail, Carolyn , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Dissertationes Mathematicae Vol. , no. 458 (2008), p.**Full Text:**false**Reviewed:****Description:**A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally compact abelian groups; (ii) the class of all k(w)-groups; (iii) the class of all sigma-compact groups; and (iv) the free abelian topological group on [0, 1]. In all cases, hierarchical containments are determined.

Iwasawa's local splitting theorem for pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****Description:**If the nilradical () of the Lie algebra of a pro-Lie group G is finite dimensional modulo the center (), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. © Walter de Gruyter 2008.**Description:**C1

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****Description:**If the nilradical () of the Lie algebra of a pro-Lie group G is finite dimensional modulo the center (), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. © Walter de Gruyter 2008.**Description:**C1

Journal of Research and Practice in Information Technology : Editorial

**Authors:**Morris, Sidney**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Research and Practice in Information Technology Vol. 41, no. 1 (2009), p. 1-2**Full Text:**false**Reviewed:**

Local splitting of locally compact groups and pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2011**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 14, no. 6 (2011), p. 931-935**Full Text:**false**Reviewed:****Description:**In the book "The Lie Theory of Connected Pro-Lie Groups" the authors proved the local splitting theorem for connected pro-Lie groups. George A. A. Michael subsequently proved this theorem for almost connected pro-Lie groups. Here his result is proved more directly using the machinery of the aforementioned book. Â© 2011 de Gruyter.

Modified neural network algorithms for predicting trading signals of stock market indices

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Applied Mathematics and Decision Sciences Vol. 2009, no. (2009), p.**Full Text:**false**Reviewed:****Description:**The aim of this paper is to present modified neural network algorithms to predict whether it is best to buy, hold, or sell shares (trading signals) of stock market indices. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The modified network algorithms are based on the structure of feed forward neural networks and a modified Ordinary Least Squares (OLSs) error function. An adjustment relating to the contribution from the historical data used for training the networks and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. These algorithms were employed to predict the trading signals of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions.

Nonmeasurable subgroups of compact groups

- Hernández, Salvador, Hofmann, Karl, Morris, Sidney

**Authors:**Hernández, Salvador , Hofmann, Karl , Morris, Sidney**Date:**2016**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 19, no. 1 (2016), p. 179-189**Full Text:****Reviewed:****Description:**In 1985 S. Saeki and K. Stromberg published the following question: Does every infinite compact group have a subgroup which is not Haar measurable? An affirmative answer is given for all compact groups with the exception of some metric profinite groups which are almost perfect and strongly complete. In this spirit it is also shown that every compact group contains a non-Borel subgroup. © 2016 by De Gruyter 2016 Generalitat Valenciana PROMETEO/2014/062 We are grateful for our referee's useful comments. In particular, the suggestion that originally we had overlooked [Pacific J. Math. 116 (1985), 217-241] shortened the proof of Theorem 4.3 considerably.

**Authors:**Hernández, Salvador , Hofmann, Karl , Morris, Sidney**Date:**2016**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 19, no. 1 (2016), p. 179-189**Full Text:****Reviewed:****Description:**In 1985 S. Saeki and K. Stromberg published the following question: Does every infinite compact group have a subgroup which is not Haar measurable? An affirmative answer is given for all compact groups with the exception of some metric profinite groups which are almost perfect and strongly complete. In this spirit it is also shown that every compact group contains a non-Borel subgroup. © 2016 by De Gruyter 2016 Generalitat Valenciana PROMETEO/2014/062 We are grateful for our referee's useful comments. In particular, the suggestion that originally we had overlooked [Pacific J. Math. 116 (1985), 217-241] shortened the proof of Theorem 4.3 considerably.

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