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

 

Absolutely closed maps


Author: Louis Friedler
Journal: Proc. Amer. Math. Soc. 51 (1975), 186-190
MSC: Primary 54C10
MathSciNet review: 0367898
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Abstract: An example is given of a continuous function $ f:X \to Y$ which is closed, has point inverses $ H$-closed, but which can be extended to a continuous function $ F:Z \to Y$ for some $ Z$ which has $ X$ as a proper dense subset. A partial characterization of nonextendable functions is given in terms similar to Bourbaki's theorem that perfect maps $ f:X \to Y$ are those for which $ f \times {i_Z}:X \times Z \to Y \times Z$ is a closed map for all spaces $ Z$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0367898-2
PII: S 0002-9939(1975)0367898-2
Keywords: $ H$-closed, absolutely closed map, regular closed map
Article copyright: © Copyright 1975 American Mathematical Society