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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Absolutely closed maps
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by Louis Friedler PDF
Proc. Amer. Math. Soc. 51 (1975), 186-190 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 186-190
  • MSC: Primary 54C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0367898-2
  • MathSciNet review: 0367898