On submetrizability and 𝐺_{𝛿}-diagonals

Mizokami, Takemi

doi:10.1090/S0002-9939-1980-0548095-6

On submetrizability and $G_{\delta }$-diagonals
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by Takemi Mizokami PDF

Proc. Amer. Math. Soc. 78 (1980), 111-115 Request permission

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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