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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 67–84 (Mi mz7724)  

This article is cited in 1 scientific paper (total in 1 paper)

An expanding system of linearly closed sets

C. G. Slobodnik

Moscow State Pedagogical Institute

Abstract: In this note it is proved that if an open cube in the Euclidean space $R^n$ can be represented in the form of the union of an expanding system of linearly closed sets, then at least one of them has an interior point. This result is applied to the investigation of real-valued functions of several variables.

Full text: PDF file (1468 kB)

English version:
Mathematical Notes, 1976, 19:1, 39–48

Bibliographic databases:

UDC: 517.5
Received: 11.03.1975

Citation: C. G. Slobodnik, “An expanding system of linearly closed sets”, Mat. Zametki, 19:1 (1976), 67–84; Math. Notes, 19:1 (1976), 39–48

Citation in format AMSBIB
\Bibitem{Slo76}
\by C.~G.~Slobodnik
\paper An expanding system of linearly closed sets
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 67--84
\mathnet{http://mi.mathnet.ru/mz7724}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=409742}
\zmath{https://zbmath.org/?q=an:0327.26011}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 39--48
\crossref{https://doi.org/10.1007/BF01147616}


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    This publication is cited in the following articles:
    1. Ciesielski K.Ch. Miller D., “A Continuous Tale on Continuous and Separately Continuous Functions”, Real Anal. Exch., 41:1 (2016), 19–54  isi
  • Математические заметки Mathematical Notes
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