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arxiv: 1805.10509 · v1 · pith:C4WVS3MOnew · submitted 2018-05-26 · 🧮 math.GN

On RC-spaces

classification 🧮 math.GN
keywords regularrc-spacesspacescompletelynormalplanearisesbase
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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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