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June 1991 The generalizations of first countable spaces
Zhu Jian-Ping
Tsukuba J. Math. 15(1): 167-173 (June 1991). DOI: 10.21099/tkbjm/1496161578

Abstract

In this paper we consider some generalizations of first countable spaces, called $w_{\kappa}$-spaces. When $\kappa=1,$ $\omega_{1},$ $\infty$, the spaces are respectively Fréchet spaces, $w$-spaces in the sense of $G$. Gruen-hage [5] and first countable spaces. We show that the $w_{\kappa}$-spaces are the images of metric spaces under certain kind of continuous maps, called $w_{\kappa}$-maps. For any cardinals $\kappa_{1} \lt \kappa_{2}$, we construct by forcing a model in which there is a countable space with character $\omega_{1}$ which is a $w_{\kappa_{1}}$-space but not $w_{\kappa_{2}}$-space.

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Zhu Jian-Ping. "The generalizations of first countable spaces." Tsukuba J. Math. 15 (1) 167 - 173, June 1991. https://doi.org/10.21099/tkbjm/1496161578

Information

Published: June 1991
First available in Project Euclid: 30 May 2017

zbMATH: 0733.54002
MathSciNet: MR1118593
Digital Object Identifier: 10.21099/tkbjm/1496161578

Rights: Copyright © 1991 University of Tsukuba, Institute of Mathematics

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Vol.15 • No. 1 • June 1991
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