Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2009; 24(2): 277-280

Printed June 1, 2009

https://doi.org/10.4134/CKMS.2009.24.2.277

Copyright © The Korean Mathematical Society.

Some remarks on centered-Lindel{\" o}f spaces

Yan-Kui Song

Nanjing Normal University

Abstract

In this paper, we prove the following two statements: (1) There exists a Hausdorff locally Lindel{\" o}f centered-Lindel{\" o}f space that is not star-Lindel{\" o}f. (2) There exists a $T_1$ locally compact centered-Lindel{\" o}f space that is not star-Lindel{\" o}f. The two statements give a partial answer to Bonanzinga and Matveev [2, Question 1].

Keywords: star-Lindel{\" o}f, centered-Lindel{\" o}f

MSC numbers: 54D20, 54G20

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