On topologies generated by Moisil resemblance relations |
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Authors: | Cristian Calude Virgil Emil Căzănescu |
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Institution: | Institute of Mathematics, Str. Academiei 14, 70109 Bucharest, Romania |
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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 ?ech 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. |
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