Spaces with property $(DC(\\omega_1))$

Commentationes mathematicae Universitatis Carolinae

Wei-feng Xuan ; Wei-xue Shi

关键词: $G_\\delta$-diagonal;    property $(DC(\\omega_1))$;    cardinal;    DCCCDOI: DOI 10.14712/1213-7243.2015.190AMS Subject Classification: 54D20 54E35 PDF;   

DOI  :  10.14712/1213-7243.2015.190

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 $\\mathfrak c$.

【 授权许可】

CC BY