FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 237-247

**On multivalued topologies on $L$-powersets of
multivalued sets**

A. P. Šostak

Abstract

View as HTML
View as gif image

Given an $M$-valued equality
$E:\; X\; \times \; X\; \to \; M$ on a set $X$, we extend it to the
$M$-valued
equality $\backslash mathcal\; E:\; LX\times \; LX\to \; M$ on the $L$-powerset $LX$
of $X$,
where $L$ is
a complete sublattice of a GL-monoid $M$.
As a result, we come to a category $$**SET**(M, L)
whose objects are quadruples $(X,\; E,\; LX,\; \backslash mathcal\; E)$.
This category serves as a ground category for the category
$L-$**TOP**(M)
of $(L,M)$-valued topological
spaces and some of its subcategories, which are the main subject of
this paper.
In particular, as special cases, we obtain here Chang--Goguen, Lowen,
Kubiak--Šostak, and some other known categories related to fuzzy
topology.

Location: http://mech.math.msu.su/~fpm/eng/k05/k054/k05419h.htm

Last modified: November 29, 2005