Semi-topological properties

Bhamini M. P. Nayar and S. P. Arya

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-6

Abstract:

A property preserved under a semi-homeomorphism is said to be a semi-topological property. In the present paper we prove the following results: (1) A topological property P is semi-topological if and only if the statement ( X , 𝒯 ) has P if and only if ( X , F ( 𝒯 ) ) has P ′ is true where F ( 𝒯 ) is the finest topology on X having the same family of semi-open sets as ( X , 𝒯 ) , (2) If P is a topological property being minimal P is semi-topological if and only if for each minimal P space ( X , 𝒯 ) , 𝒯 = F ( 𝒯 ) .

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:867864

DOI: 10.1155/S0161171292000346

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