2017
Том 69
№ 9

All Issues

One-Point Discontinuities of Separately Continuous Functions on the Product of Two Compact Spaces

Mykhailyuk V. V.

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Abstract

We investigate the existence of a separately continuous function $f :\; X \times Y \rightarrow \mathbb{R}$ with a one-point set of points of discontinuity in the case where the topological spaces $X$ and $Y$ satisfy conditions of compactness type. In particular, for the compact spaces $X$ and $Y$ and the nonizolated points $x_0 \in X$ and $y_0 \in Y$, we show that the separately continuous function $f :\; X \times Y \rightarrow \mathbb{R}$ with the set of points of discontinuity $\{(x_0, y_0)\}$ exists if and only if sequences of nonempty functionally open set exist in $X$ and $Y$ and converge to $x_0$ and $y_0$, respectively.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 1, pp 112-120.

Citation Example: Mykhailyuk V. V. One-Point Discontinuities of Separately Continuous Functions on the Product of Two Compact Spaces // Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 94–101.

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