Geodesic
Spaces with property $(DC(\omega_1))$
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 131-135.

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We prove that if $X$ is a first countable space with property $(DC(\omega_1))$ and with a $G_\delta$-diagonal then the cardinality of $X$ is at most $\mathfrak c$. We also show that if $X$ is a first countable, DCCC, normal space then the extent of $X$ is at most $\mathfrak c$.
DOI : 10.14712/1213-7243.2015.190
Classification : 54D20, 54E35
Keywords: $G_\delta$-diagonal; property $(DC(\omega_1))$; cardinal; DCCC 
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Xuan, Wei-Feng; Shi, Wei-Xue. Spaces with property $(DC(\omega_1))$. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 131-135. doi : 10.14712/1213-7243.2015.190. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.190/

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