Algebra, Logic and Topology

 

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Author(s)
Dirk Hofmann; Gonçalo Gutierres;

Title
Axioms for sequential convergence

Abstract
It is of general knowledge that those (ultra)filter 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 Kisynski (Colloq. Math. 7:205–211, 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 (Bechyne, 1984), Math. Res., vol. 24, pp. 199–204, Akademie-Verlag, 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.

Journal
Applied Categorical Structures

Volume
15

Year
2007

Issue
5-6

Page(s)
599-614

 
     
 

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