On the connectedness of boundary and complement for domains

Volume 103 / 2011

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski Annales Polonici Mathematici 103 (2011), 189-191 MSC: Primary 57N15; Secondary 54D05. DOI: 10.4064/ap103-2-6

Abstract

This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in $\mathbb R^n$ is equivalent to the connectedness of its complement.

Authors

  • Andrzej CzarneckiInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Marcin KulczyckiInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Wojciech LubawskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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