Axioms for Sequential Convergence |
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Authors: | Gonçalo Gutierres Dirk Hofmann |
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Institution: | (1) Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal;(2) Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal |
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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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Keywords: | Convergence Sequence Sequential space Monad |
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