# On multivalued topologies on L-powersets of multivalued sets

Research paper by Alexander Šostak

Indexed on: 01 Aug '07Published on: 01 Aug '07Published in: Journal of Mathematical Sciences

#### Abstract

Given an M-valued equality E: X×X → M on a set X, we extend it to the M-valued equality ε: 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, ε). 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.