A note on M₁-spaces

Kuo Shih Kao

Vol. 108 (1983), No. 1, 121–128

DOI: 10.2140/pjm.1983.108.121

Abstract

A mapping f : X → Y is called quasi-open if the interior of f(U) is non-void for any non-void open subsets U of X. The main result in this paper is that the image of an M₁-space under a quasi-open, countably bi-quotient closed mapping is an M₁-space; it follows that the locally finite regular closed sum of M₁-spaces is an M₁-space.

Mathematical Subject Classification 2000

Primary: 54E20

Secondary: 54C10

Milestones

Received: 22 December 1981

Revised: 10 May 1982

Published: 1 September 1983