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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pseudo-open mappings from topological sums


Author: Dennis K. Burke
Journal: Proc. Amer. Math. Soc. 74 (1979), 191-196
MSC: Primary 54E30
MathSciNet review: 521897
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0521897-X
PII: S 0002-9939(1979)0521897-X
Keywords: Compatible family of topologies, pseudo-open map, quasi-developable, developable, $ \sigma $-disjoint base, subparacompact
Article copyright: © Copyright 1979 American Mathematical Society