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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 69, Issue 2


A note on discrete C-embedded subspaces

Mehrdad Namdari / Mohammad Ali Siavoshi
Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ms-2017-0239


It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are C-embedded. In particular, this generalizes the well-known fact that every countable subset of P-spaces are C-embedded. In the presence of the measurable cardinals, we observe that if X is a discrete space then every subspace of υ X (i.e., the Hewitt realcompactification of X) whose cardinal is nonmeasurable, is a C-embedded, discrete realcompact subspace of υ X. This generalizes the well-known fact that the discrete spaces with nonmeasurable cardinal are realcompact.

MSC 2010: 54A25; 54C30; 54D60

Keywords: C-embedded; realcompact spaces; Pλ-spaces; socle; isolated points; essential ideals


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About the article

Dedicated to professor O. A. S. Karamzadeh on the occasion of his retirement and to appreciate his unique and inimitable style for activities in mathematics (including his profound and indelible influence that has had on many people all around the country, his passion and loving, teaching, talking, sharing, and doing mathematics) for nearly half a century in Iran.

Received: 2018-02-25

Accepted: 2018-05-23

Published Online: 2019-03-19

Published in Print: 2019-04-24

(Communicated by Ľubica Holá)

Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 469–473, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0239.

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