Abstract
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 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,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-Šostak, and some other known categories related to fuzzy topology.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 237–247, 2005.
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Šostak, A. On multivalued topologies on L-powersets of multivalued sets. J Math Sci 144, 4527–4534 (2007). https://doi.org/10.1007/s10958-007-0292-1
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DOI: https://doi.org/10.1007/s10958-007-0292-1