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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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Keywords: <IMG WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$H$">-closed, absolutely closed map, regular closed map
Article copyright: © Copyright 1975 American Mathematical Society