One-point discontinuities of separately continuous functions on the product of two compact spaces

被引：0

作者：

Mykhailyuk V.V. ^{[1
]}

机构：

[1] Chernivtsi University, Chernivtsi

来源：

Ukrainian Mathematical Journal | 2005年 / 57卷 / 1期

关键词：

Continuous Function; Topological Space; Compact Space; Discontinuity Point; Compactness Type;

D O I：

10.1007/s11253-005-0174-y

中图分类号：

学科分类号：

摘要：

We investigate the existence of a separately continuous function f: X × Y → ℝ with a one-point set of discontinuity points in the case where the topological spaces X and Y satisfy conditions of compactness type. In particular, it is shown that, for compact spaces X and Y and nonisolated points x 0 X and y 0 Y, a separately continuous function f: X × Y → ℝ with the set of discontinuity points {(x 0, y 0)} exists if and only if there exist sequences of nonempty functionally open sets in X and Y that converge to x 0 and y 0, respectively. © 2005 Springer Science+Business Media, Inc.

引用

页码：112 / 120

页数：8

共 10 条

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