Short notes

Normal functors on the category of paracompact $p$-spaces and their perfect mappings

M. A. Dobrinina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: It is proved that for any paracompact $p$-space $X$ and any normal functor ${\mathscr F}$ of degree $\geq3$ in the category $\mathscr{P}$ the hereditary normality of the space $\mathscr{F}(X) \setminus X$ implies the metrizability of $X$.

Key words: paracompact $p$-space, normal functor, hereditary normality, metrizability.

UDC: 515.12

Received: 16.12.2011

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2012, 67:4, 185–187

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