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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 1, Pages 35–46
DOI: https://doi.org/10.1070/SM1973v019n01ABEH001734
(Mi sm2994)
 

This article is cited in 2 scientific papers (total in 2 papers)

On $p$-spaces and their continuous maps

N. V. Velichko
References:
Abstract: The following theorems are the main results of this paper.
Theorem 1. Let $f\colon X\to Y$ be a closed mapping of the weakly paracompact $p$-space $X$. In order that the space $Y$ be weakly paracompact and plumed, it is necessary and sufficient that the mapping $f$ be peripherally bicompact. \smallskip
Theorem 2. {\it Let $f\colon X\to Y$ be a closed mapping of a weakly paracompact $p$-space $X$. Then $Y=Y_0\cup Y_1,$ where the set $Y_1$ is $\sigma$-discrete in $Y$ and the set $f^{-1}y$ is bicompact for each point $y\in Y_0$.}
An example is constructed of a weakly paracompact, locally compact, $\sigma$-paracompact space which is not normal and which cannot be mapped perfectly onto a space with a refining sequence of coverings.
Bibliography: 22 titles.
Received: 29.01.1972
Bibliographic databases:
UDC: 513.83
MSC: Primary 54G10, 54C10; Secondary 54D20
Language: English
Original paper language: Russian
Citation: N. V. Velichko, “On $p$-spaces and their continuous maps”, Math. USSR-Sb., 19:1 (1973), 35–46
Citation in format AMSBIB
\Bibitem{Vel73}
\by N.~V.~Velichko
\paper On $p$-spaces and their continuous maps
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 1
\pages 35--46
\mathnet{http://mi.mathnet.ru//eng/sm2994}
\crossref{https://doi.org/10.1070/SM1973v019n01ABEH001734}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=339082}
\zmath{https://zbmath.org/?q=an:0252.54005}
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  • https://doi.org/10.1070/SM1973v019n01ABEH001734
  • https://www.mathnet.ru/eng/sm/v132/i1/p34
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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