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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
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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Keywords: Compactly closed sets, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$k$">-space, proper map, local homeomorphism, covering projection, homotopy lifting property
Article copyright: © Copyright 1975 American Mathematical Society