In this chapter we describe a fuzzy filter functor in a general framework of set functors. The
general theory includes generalized Cauchy spaces, together with a construction for …

It is the purpose of this paper to have a look at fuzzy topology from the point of view of
categorical topology. We first look at interesting subcategories of FTS and determine …

This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory
held each September in Linz, Austria. First, this volume is an extended account of the …

The Historical Development of Uniform, Proximal, and Nearness Concepts in Topology |
SpringerLink Skip to main content Advertisement SpringerLink Account Menu Find a journal …

In previous papers, various notions of (strongly) closed subobject,(strongly) open subobject,
connected, compact and T i, i= 0, 1, 2 objects in a topological category were introduced and …

Conv S, the category of symmetric convergence spaces, and Chy, the category of Cauchy
spaces, are embedded as full subcategories of Katětov's category, Fil, of filter merotopic …

In a fuzzy topology on a set X, the limit of a prefilter (ie a filter in the lattice [0, i] X) is
calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology …

It is shown that the category Chy of Cauchy spaces is a cartesian closed topological
category. Hence quotient maps in Chy are finitely productive. Examples are provided which …

We develop the completion theories for regular nearness spaces as well as for regular
Cauchy spaces and we describe the respective suitable classes of maps such that …

There are various generalization of the usual topological T3 and T4 axioms to topological
categories defined in [2] and [7].[7] is shown that they lead to different T3 and T4 concepts, in …