On RC-spaces
General Topology
2018-05-29 v1
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.
Keywords
Cite
@article{arxiv.1805.10509,
title = {On RC-spaces},
author = {Wojciech Bielas and Szymon Plewik},
journal= {arXiv preprint arXiv:1805.10509},
year = {2018}
}