A Category of L-Fuzzy Convergence Spaces

Abstract

In this paper we take convergence of stratified L-filters
as a primitive notion and construct in this way a Cartesian closed category,
which contains the category of stratified L-topological spaces as reflexive
subcategory. The class of spaces with non-idempotent stratified fuzzy interior
operator is characterized as subclass of the class of our stratified L-fuzzy
convergence spaces and a first characterization, which fuzzy convergences stem
from stratified L-topologies is established.
Mathematics Subject Classification (2000): 54A40
Keywords: category, L-filter, fuzzy convergence, L-Topological space,
function space, fuzzy topology, L-topology, convergence, closed categories,
categories, interior operator, convergence spaces



Quaestiones Mathematicaes 24 (4) 2001, 500–517