Research Papers Dedicated to the 100th Anniversary of P. S. Alexandroff's Birth

On $\varkappa$-closed images of subsets of topological products

K. L. Kozlov

M. V. Lomonosov Moscow State University

Abstract: It is proved that a first countable $\varkappa$-closed image of a $G_\delta$-dense subset of the product of metric spaces is metrizable. It is also proved that the subset of points the internal of which prototype is not empty is a $\sigma$-discreet set in the $\varkappa$-closed image of some subsets of the Tychonoff product of spaces with $\sigma$-discreet $\pi$-base, and the boundary of a prototype of a $q$-point of image is relatively pseudocompact, if the image is a $\varkappa$-closed image of some subsets of topological product of Dieudonne complete spaces.

UDC: 515.12

Received: 01.02.1997

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