International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 497-511
doi:10.1155/S0161171285000540
Characterization of convergence in fuzzy topological spaces
1Department of Mathematics, Free University of Brussels, Brussels 1050, Belgium
2Dienst Wiskundige Analyse, University of Antwerp, R.U.C.A. 2020, Antwerp, Belgium
Received 19 March 1985
Copyright © 1985 E. Lowen and R. Lowen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule “lim” which to any prefilter 𝔇 on X assigns, a function lim𝔇∈[0,1]X. We give necessary and sufficient conditions for the function 𝔇→lim𝔇 in order that it can be derived from a fuzzy topology.