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. Nayar1,2 and S. P. Arya1,2

1Department of Mathematics, Howard University, Washington. DC 20059, USA
2Maitreyi College, Netaji Nagar, New Delhi 11023, India

Received 13 July 1990; Revised 11 April 1991

Copyright © 1992 Bhamini M. P. Nayar and S. P. Arya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).