International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 267-272
doi:10.1155/S0161171292000346
Semi-topological properties
Bhamini M.P. Nayar
and S.P. Arya
Department of Mathematics, Howard University, Washington. DC 20059, USA
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).