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 × X → M on a set X, we extend it to the M-valued equality \mathcal E: LX × LX → 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, \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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