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240101 Pure Mathematics
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3Abelian topological group
3Banach space
3Exponential function
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3Quotient group
3Separable quotient problem
3Topological group
20199 Other Mathematical Sciences
20802 Computation Theory and Mathematics
2Compact 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:**

Subspaces of the free topological vector space on the unit interval

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2018**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 97, no. 1 (2018), p. 110-118**Full Text:**false**Reviewed:****Description:**For a Tychonoff space X, let V(X) be the free topological vector space over X, A(X) the free abelian topological group over X and I the unit interval with its usual topology. It is proved here that if X is a subspace of I, then the following are equivalent: V(X) can be embedded in V(I) as a topological vector subspace; A(X) can be embedded in A(I) as a topological subgroup; X is locally compact. © 2017 Australian Mathematical Publishing Association Inc..

Open mapping theorem for topological groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 31, no. 2 (2007), p. 533-551**Full Text:**false**Reviewed:****Description:**We survey sufficient conditions that force a surjective continuous homomorphism between topological groups to be open. We present the shortest proof yet of an open mapping theorem between projective limits of finite dimensional Lie groups.**Description:**C1**Description:**2003005915

The structure of almost connected pro-lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2011**Type:**Text , Journal article**Relation:**Journal of Lie Theory Vol. 21, no. 2 (2011), p. 347-383**Full Text:**false**Reviewed:****Description:**Recalling that a topological group G is said to be almost connected if the quotient group G=G0 is compact, where G0 is the connected component of the identity, we prove that for an almost connected pro-Lie group G, there exists a compact zero-dimensional, that is, profinite, subgroup D of G such that G = G0D. Further for such a group G, there are sets I , J , a compact connected semisimple group S , and a compact connected abelian group A such that G and ℝI × (ℤ=2ℤ)J × S × A are homeomorphic. En route to this powerful structure theorem it is shown that the compact open topology makes the automorphism group Aut g of a semisimple pro-Lie algebra g a topological group in which the identity component (Aut g)0 is exactly the group Inn g of inner automorphisms. In this situation, Inn(G) has a totally disconnected semidirect complement

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

The Structure of Compact Groups : A primer for students - A handbook for the expert

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2006**Type:**Text , Book**Full Text:**false**Description:**Dealing with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. The first edition of 1998 was well received by reviewers and has been frequently quoted in the areas of instruction and research. For the present new edition, the text has been improved in various sections. New material has been added in order to reflect ongoing research.**Description:**2003002192

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

On the pro-lie group theorem and the closed subgroup theorem

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Lie Theory Vol. 18, no. 2 (2008), p. 383-390**Full Text:**false**Reviewed:****Description:**Let H and M be closed normal subgroups of a pro-Lie group G and assume that H is connected and that G/M is a Lie group. Then there is a closed normal subgroup N of G such that N ? M, that G/N is a Lie group, and that HN is closed in G. As a consequence, H/(H ? N) ? HN/N is an isomorphism of Lie groups. © 2008 Heldermann Verlag.**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:**

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Book**Full Text:**false**Reviewed:****Description:**A1**Description:**2003005498

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

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

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:**

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

Quantification of intermarket influence on the Australian All Ordinary Index based on optimization techniques

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

**Authors:**Tilakaratne, Chandima , Morris, Sidney , Mammadov, Musa , Hurst, Cameron**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at CTAC 2006: The 13th Biennial Computational Techniques and Applications Conference p. 42-49**Full Text:****Reviewed:**

**Authors:**Tilakaratne, Chandima , Morris, Sidney , Mammadov, Musa , Hurst, Cameron**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at CTAC 2006: The 13th Biennial Computational Techniques and Applications Conference p. 42-49**Full Text:****Reviewed:**

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

The structure of abelian pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2004**Type:**Text , Journal article**Relation:**Mathematische Zeitschrift Vol. 248, no. 4 (Dec 2004), p. 867-891**Full Text:**false**Reviewed:****Description:**A pro-Lie group is a projective limit of a projective system of finite dimensional Lie groups. A prodiscrete group is a complete abelian topological group in which the open normal subgroups form a basis of the filter of identity neighborhoods. It is shown here that an abelian pro-Lie group is a product of (in general infinitely many) copies of the additive topological group of reals and of an abelian pro-Lie group of a special type; this last factor has a compact connected component, and a characteristic closed subgroup which is a union of all compact subgroups; the factor group modulo this subgroup is pro-discrete and free of nonsingleton compact subgroups. Accordingly, a connected abelian pro-Lie group is a product of a family of copies of the reals and a compact connected abelian group. A topological group is called compactly generated if it is algebraically generated by a compact subset, and a group is called almost connected if the factor group modulo its identity component is compact. It is further shown that a compactly generated abelian pro-Lie group has a characteristic almost connected locally compact subgroup which is a product of a finite number of copies of the reals and a compact abelian group such that the factor group modulo this characteristic subgroup is a compactly generated prodiscrete group without nontrivial compact subgroups.**Description:**C1**Description:**2003000910

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.

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