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

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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.

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Last modified: November 29, 2005