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On RC-spaces


Following Frink’s characterization of completely regular spaces, we say that a regular \(T_1\)-space is an RC-space whenever the family of all regular open sets constitutes a regular normal base. Normal spaces are RC-spaces and there exist completely regular spaces which are not RC-spaces. So the question arises, which of the known examples of completely regular and not normal spaces are RC-spaces. We show that the Niemytzki plane and the Sorgenfrey plane are RC-spaces.


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Correspondence to Wojciech Bielas.

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Bielas, W., Plewik, S. On RC-spaces. Arab. J. Math. 9, 83–88 (2020).

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Mathematics Subject Classification

  • 54D15
  • 54G20