## Wei-feng Xuan, Wei-xue ShiSpaces with property $(DC(\omega_1))$

Comment.Math.Univ.Carolin. 58,1 (2017) 131-135.

Abstract: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 $\mathfrak c$.

Keywords: $G_\delta$-diagonal; property $(DC(\omega_1))$; cardinal; DCCC

DOI: DOI 10.14712/1213-7243.2015.190
AMS Subject Classification: 54D20 54E35

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