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Proceedings of the American Mathematical Society

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



Products of a compact space and a metric space

Author: Yukinobu Yajima
Journal: Proc. Amer. Math. Soc. 101 (1987), 577-581
MSC: Primary 54B10; Secondary 54C10, 54C15, 54E35
MathSciNet review: 908672
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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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Keywords: Compact space, metric space, product, closed map, perfect map, Lašnev space, $ {G_\delta }$-diagonal, neighborhood retract
Article copyright: © Copyright 1987 American Mathematical Society

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