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0101 Pure Mathematics

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Date: 2017
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159323
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 homeomorph... More
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Date: 2017
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/156253
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) c... More
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Date: 2017
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154574
Description: In 1983 P. Domanski investigated the question: For which separable topological vector spaces E, does the separable space have a nonseparable closed vector subspace, where is the cardinality of the con... More
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Date: 2017
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/156932
Description: A class of abelian topological groups was previously defined to be a variety of topological groups with coproducts if it is closed under forming subgroups, quotients, products and coproducts in the ca... More
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Date: 2017
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155253
Description: In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are inves... More
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154692
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.
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100317
Description: In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their ... More
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99916
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 group... More
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102916
Description: This paper concerns a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/firms who sha... More
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154479
Description: We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of t... More
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Date: 2016
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102487
Description: In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level... More
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Date: 2015
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/89653
Description: Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, fo... More
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Date: 2015
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100313
Description: We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the ... More
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Date: 2015
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/89643
Description: Epi/hypo convergence of finite-valued bivariate functions defined on the product of two subsets, with some connections to lopsided convergence, is considered. Namely, we deal with three full character... More
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Date: 2015
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155338
Description: The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extend... More
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