Inductively perfect maps and tri-quotient maps

Michael, E.

doi:10.1090/S0002-9939-1981-0603613-5

Inductively perfect maps and tri-quotient maps
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Proc. Amer. Math. Soc. 82 (1981), 115-119 Request permission

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.

References

Erweiterung einer Homöomorphie

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