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Proceedings of the American Mathematical Society

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

 

 

On submetrizability and $ G\sb{\delta }$-diagonals


Author: Takemi Mizokami
Journal: Proc. Amer. Math. Soc. 78 (1980), 111-115
MSC: Primary 54E35; Secondary 54B20, 54C10
MathSciNet review: 548095
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Abstract: Open perfect maps and open compact maps with the property that the collection of all nontrivial fibers is discrete are shown to preserve submetrizability and if $ f:X \to Y$ is an open compact or perfect map with the above property such that the union of all nontrivial fibers is $ {G_\delta }$ and if X has a $ \overline {{G_\delta }(1)} $-diagonal, then Y is shown to have a $ {G_\delta }$-diagonal.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0548095-6
Keywords: Submetrizable, $ {G_\delta }$-diagonal, perfect map
Article copyright: © Copyright 1980 American Mathematical Society