Pseudo-Open Mappings from Topological Sums

Abstract

Assume S is the free topological sum of spaces ${X_1}$ and ${X_2}$, on the same set X, and $\phi :S \to X$ is the canonical quotient map. The main result states that X is developable (resp. quasi-developable) if ${X_1}$ and ${X_2}$ are regular developable (resp. quasi-developable) spaces and $\phi$ is pseudo-open. Examples are given to show that certain topological properties are not preserved under such a construction.