ON MULTIVALUED TOPOLOGIES ON L-POWERSETS OF MULTIVALUED SETS

摘要

Given an M-valued equality E: X × X → M on a set X, we extend it to the M-valued equality ε: L~x × L~x → M on the L-powerset L~x of X, where I, 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, L~x, 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-Sostak, and some other known categories related to fuzzy topology.