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Categorical properties of \(M\)-indiscernibility spaces. (English) Zbl 1225.03069

Summary: This paper discusses categorical aspect of Pawlak’s rough set theory. It is proved that the category of all \(M\)-indiscernibility spaces and \(M\)-equivalence relation-preserving mappings between them is both a topological construct and a topos. As an application of these results, the notions of product \(M\)-indiscernibility space, sum \(M\)-indiscernibility space, quotient \(M\)-indiscernibility space, \(M\)-indiscernibility subspace, quotient mapping, and isomorphism mapping are defined, and structures of these \(M\)-indiscernibility spaces and mappings are also given.

MSC:

03E72 Theory of fuzzy sets, etc.
18B25 Topoi
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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