## Perfect maps of symmetrizable spaces

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- by Harold W. Martin
- Proc. Amer. Math. Soc.
**38**(1973), 410-412 - DOI: https://doi.org/10.1090/S0002-9939-1973-0314009-3
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## Abstract:

It is shown that if $f:X \to Y$ is a perfect map from a symmetrizable space $X$ onto a space $Y$, then $Y$ is metrizable if and only if $f$ is a coherent map. This fact, together with certain known results, yields the following: Let $f:X \to Y$ be a perfect map from a Hausdorff symmetrizable space $X$ onto a space $Y$; the following are equivalent: (1) $X$ is metrizable; (2) $f$ is a regular map; (3) $f$ is a coherent map; (4) $Y$ is metrizable.## References

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## Bibliographic Information

- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**38**(1973), 410-412 - MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1973-0314009-3
- MathSciNet review: 0314009