A co-topological application to minimal spaces
Giovanni Viglino · Pacific Journal of Mathematics · 1968
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' S ~} = 0 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.Notation.Let β be an open base for the space (X, τ).τ β will denote the topology on X generated by the subbase {X\Cl τ B \Be β}.REMARK.J. de Groot in his investigation for a general classification of Baire spaces considered the above topologies (cf.[1], [4]).These topologies have come to be known as co-topologies.DEFINITIONS.A filter base is regular if it is open and equivalent to a closed filter base.