On topologies generated by Moisil resemblance relations

✍ Scribed by Cristian Calude; Virgil Emil Căzănescu

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 692 KB
• Volume: 25
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(79)90012-8

✦ Synopsis

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 tech 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.