Products of a compact space and a metric space

Yajima, Yukinobu

doi:10.1090/S0002-9939-1987-0908672-3

Products of a compact space and a metric space
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Proc. Amer. Math. Soc. 101 (1987), 577-581 Request permission

Abstract:

Let $X \times Y$ be the product of a compact space $X$ and a metric space $Y$. We consider a continuous closed image $Z$ of $X \times Y$. Moreover, we consider a closed subspace $R$ in $X \times Y$ which is a neighborhood retract of it. It is proved in this paper that $Z$ (respectively, $R$) is a Lašnev (metrizable) space iff all compact subspaces of $Z\left ( R \right )$ are metrizable.

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