(WEAK) COMPACTNESS AND LOCAL (WEAK) COMPACTNESS IN FUZZY PREUNIFORM CONVERGENCE SPACES

Abstract

Using fuzzy filters in the sense of P. Eklund and W. G¨ahler [2] in fuzzy preuniform convergence spaces as introduced in [11] compactness and weak compactness are presented by means of convergence and preconvergence of fuzzy ultrafilters respectively. The generalization of these concepts by localization leads to bicoreflective subconstructs of the construct of FPUConv of fuzzy preuniform convergence spaces which are additionally cartesian closed. These results are even new in the non-fuzzy case (i.e. in the realm of preuniform convergence spaces) which is included and improve the situation for topological spaces.