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Proceedings of the American Mathematical Society

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

 
 

 

Inductively perfect maps and tri-quotient maps


Author: E. Michael
Journal: Proc. Amer. Math. Soc. 82 (1981), 115-119
MSC: Primary 54C10; Secondary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1981-0603613-5
MathSciNet review: 603613
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Abstract: It is proved that every tri-quotient map $ f:X \to Y$ from a metric space $ X$ onto a countable regular space $ Y$, with each $ {f^{ - 1}}(y)$ completely metrizable, is inductively perfect. It is not known to what extent all the hypotheses in this result are necessary, and that leads to some open questions regarding simple compactness properties of mappings between separable metric spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0603613-5
Keywords: Inductively perfect, tri-quotient, compact-covering, countable-compact-covering
Article copyright: © Copyright 1981 American Mathematical Society

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