Semi-topological properties - Bhamini M. P. Nayar; S. P. Arya (International Journal of Mathematics and Mathematical Sciences)
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).