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Title of Journal: Appl Categor Struct

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Abbravation: Applied Categorical Structures

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Springer Netherlands

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DOI

10.1007/BF03266588

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1572-9095

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Axioms for Sequential Convergence

Authors: Gonçalo Gutierres Dirk Hofmann
Publish Date: 2007/07/11
Volume: 15, Issue: 5-6, Pages: 599-614
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Abstract

It is of general knowledge that those ultrafilter convergence relations coming from a topology can be characterized by two natural axioms However the situation changes considerable when moving to sequential spaces In case of unique limit points Kisyński Colloq Math 7205–211 1959/1960 obtained a result for sequential convergence similar to the one for ultrafilters but the general case seems more difficult to deal with Finally the problem was solved by Koutnik Closure and topological sequential convergence In Convergence Structures 1984 Bechyně 1984 Math Res vol 24 pp 199–204 AkademieVerlag Berlin 1985 In this paper we present an alternative approach to this problem Our goal is to find a characterization more closely related to the case of ultrafilter convergence We extend then the result to characterize sequential convergence relations corresponding to Fréchet topologies as well to those corresponding to pretopological spaces

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  2. Complexity Analysis via Approach Spaces
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  10. A Generalization of De Vries Duality Theorem
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  12. Normal Subgroups of B u Aut(Ω)
  13. Lawvere Completeness in Topology
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