Axioms for Sequential Convergence

: 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 J. Kisy´nski [Kis60] 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 V. Koutnik [Kou85]. In this paper we present an alternative approach to this problem. Our goal is to find a characterization more related to the case of ultrafilter convergence. We extend then the result to characterize sequential convergence relations corresponding to Fr´echet topologies, as well to those corresponding to pretopological spaces.

• Type: Journal
• Year: 2007
• Where: ACS
• Authors: Gonçalo Gutierres, Dirk Hofmann
• Keywords: ACS 2007, Convergence Relations, Distributed And Parallel Computing, Sequential Convergence, filter Convergence Relations