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Axioms for Sequential Convergence

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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 Kisyński (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 (Bechyně, 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.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Coimbra, 3001-454, Coimbra, Portugal

    Gonçalo Gutierres

  2. Departamento de Matemática, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    Dirk Hofmann

Authors
  1. Gonçalo Gutierres
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  2. Dirk Hofmann
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Correspondence to Dirk Hofmann.

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Gutierres, G., Hofmann, D. Axioms for Sequential Convergence. Appl Categor Struct 15, 599–614 (2007). https://doi.org/10.1007/s10485-007-9095-2

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  • DOI: https://doi.org/10.1007/s10485-007-9095-2

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