(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 127-134

## On $\kappa$-closed images of subsets of topological products

K. L. Kozlov

Abstract

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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.

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