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

Weak normality of $2^{X}$ and of $X^{\tau}$

A. P. Kombarov

M. V. Lomonosov Moscow State University

Abstract: It is proved that a weak normality of a space of closed subsets of a countably compact space $X$ implies that $X$ is compact. The example shows that the countable compactness of $X$ is essential. It is also proved that a weak normality of a sufficiently large power of $X$ implies that $X$ is compact.

UDC: 515.12

Received: 01.12.1996

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