Title: On topologies generated by Moisil resemblance relations
Abstract: In [8] and [9] Moisil has introduced the resemblance relations. Following [9] we associate to every resemblance relation an extensive operator which commutes with arbitrary unions of sets. We are leading to consider spaces endowed with such closure operators; we shall call these spaces total Čech spaces (TC-spaces). TC-spaces are in one-to-one, onto correspondence with reflexive relations. TC-spaces generated by transitive relations are in one-to-one, onto correspondence with the total topological spaces of W. Hartnett (which are called total Kuratowski spaces, TK-spaces). We study the category of TC-spaces and its full subcategory determined by TK-spaces. Both categories are Cartesian closed, but they are not elementary toposes.
Publication Year: 1979
Publication Date: 1979-02-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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