On variants of θ-Menger spaces

Abstract

In this paper we futher study θ-Menger, θ-almost Menger and θ-weakly Menger properties [13] and investigate their relationships with other selective covering properties. It is shown that for an extremally disconnected semi-regular space, the properties viz. Menger, semi-Menger, α-Menger, θ-Menger, midly Menger are equivalent. It is also proved that for an extremally disconnected space X, every finite power of X has the selection property Sf in(θ-O, θ-O) if and only if X has the property Sf in(θ-Ω, θ-Ω). We further characterize θ-Menger and θ-almost Menger properties and also discuss the preservation properties of θ-almost Menger property under various type of maps.