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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on proper maps


Author: Chung Wu Ho
Journal: Proc. Amer. Math. Soc. 51 (1975), 237-241
MSC: Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1975-0370471-3
MathSciNet review: 0370471
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Abstract: The author establishes some necessary and sufficient conditions on a Hausdorff space $ Y$ which force every open proper map into $ Y$ to be surjective. Using this result, the author then shows that a local homeomorphism from a path connected space into a simply connected space is a global homeomorphism onto if and only if the map is proper.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0370471-3
Keywords: Compactly closed sets, $ k$-space, proper map, local homeomorphism, covering projection, homotopy lifting property
Article copyright: © Copyright 1975 American Mathematical Society

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