P-EXPANDABLE SPACES

Abstract

We introduce the concept of P-expandable spaces as a variation of expandable spaces.  A space (X, τ) is said to be P-expandable if every locally finite collection \(\mathcal{F}\) = {F_α : α ∈ ∆} of subsets of X there exists a p-locally finite collection \(\mathcal{G}\) = {G_α : α ∈ ∆} of preopen subsets of X such that F_α ⊆ G_α for each α ∈ ∆.  We characterize P-expandable spaces and study their basic properties.  We show that if a space (X, τ) is a quasi submaximal space, then (X, τ) is P-expandable if and only if it is expandable.