Short notes

The uniformly normal spaces

A. V. Bogomolov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A topological space $X$ is uniformly normal if the family $\mathcal{ U}$ of all symmetric neighborhoods of the diagonal $\Delta \subset X\times X$ forms a uniformity on $X$. A neighborhood of the diagonal is any subset whose interior contains the diagonal. It is proved that the $\Sigma$-product of Lindelof $p$-spaces of countable tightness is uniformly normal.

Key words: uniform normality, uniformity, $\Sigma$-product, countable tightness, $F_\sigma$-$\delta$-normality.

UDC: 515.12

Received: 18.05.2015

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2016, 71:4, 170–171

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