## 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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### References:

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