Mappings and decompositions of continuity on almost Lindelöf spaces

Abstract

A topological space X is said to be almost Lindelöf if for every open cover {Uα : α ∈ Δ} of X there exists a countable subset {αn : n ∈ ℕ}⊆Δ such that . In this paper we study the effect of mappings and some decompositions of continuity on almost Lindelöf spaces. The main result is that a image of an almost Lindelöf space is almost Lindelöf.