On RC-spaces

Wojciech Bielas; Szymon Plewik

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arXiv · 1805.10509

On RC-spaces

Wojciech Bielas·Szymon Plewik

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Abstract

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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Wojciech Bielas, Szymon Plewik. 2018-05-26. On RC-spaces. https://arxiv.org/abs/1805.10509

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