A co-topological application to minimal spaces

Giovanni Viglino

Vol. 27 (1968), No. 1, 197–200

DOI: 10.2140/pjm.1968.27.197

Abstract

A space (X,τ) which satisfies a topological property P is said to be minimal-P if T = {τ′∣τ′ is a P-topology on X;τ′ ≨ τ} = ∅. For example, a Hausdorff space (X,τ) is minimal Hausdorff if there exists no Hausdorff topology on X which is strictly weaker than τ. The purpose of this paper is to show that for certain properties one need only consider a subset of T “induced” by τ to determine if (X,τ) is minimal-P.

Mathematical Subject Classification

Primary: 54.20

Milestones

Received: 23 August 1967

Revised: 20 October 1967

Published: 1 October 1968