Pseudo-open mappings from topological sums

Burke, Dennis K.

doi:10.1090/S0002-9939-1979-0521897-X

Pseudo-open mappings from topological sums
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by Dennis K. Burke

Proc. Amer. Math. Soc. 74 (1979), 191-196

DOI: https://doi.org/10.1090/S0002-9939-1979-0521897-X

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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.

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On pseudo-open mappings of paracompact spaces

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