publication . Preprint . 2018

On RC-spaces

Bielas, Wojciech; Plewik, Szymon;
Open Access English
  • Published: 26 May 2018
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.
Subjects
free text keywords: Mathematics - General Topology, Primary: 54, Secondary: 05
Download from

[1] D. Chodounsky´, Non-normality and relative normality of Niemytzki plane. Acta Univ. Carolin. Math. Phys. 48 (2007), no. 2, 37-41. [OpenAIRE]

[2] R. Engelking, General topology. Mathematical Monographs, Vol. 60, PWNPolish Scientific Publishers, Warsaw, (1977).

[3] O. Frink, Compactifications and semi-normal spaces. Amer. J. Math. 86 1964 602-607. [OpenAIRE]

[4] F. B. Jones, Hereditarily separable, non-completely regular spaces, Proceedings of the Blacksburg Virginia Topological Conference, March (1973).

[5] P. Kalemba and Sz. Plewik, On regular but not completely regular spaces, arXiv:1701.04322.

[6] A. K. Misra, Some regular Wallman βX, Nederl. Akad. Wetensch. Proc. Ser. A 76=Indag. Math. 35 (1973), 237-242.

[7] A. Mysior, A regular space which is not completely regular. Proc. Amer. Math. Soc. 81 (1981), no. 4, 652-653. [OpenAIRE]

[8] L.A. Steen and J.A.jun. Seebach, Counterexamples in topology. New York etc.: Holt, Rinehart and Winston, Inc., XIII, (1970).

[9] A. Zame, A note on Wallman spaces. Proc. Amer. Math. Soc. 22 (1969) 141- 144. Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice [OpenAIRE]

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue