期刊论文详细信息
Commentationes mathematicae Universitatis Carolinae | |
Metrization of function spaces with the Fell topology | |
Hanbiao Yang1  | |
关键词: space of continuous maps; Fell topology; hyperspace; metrizable; hypograph; separable; first-countable; | |
DOI : | |
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 】
For a Tychonoff space $X$, let $\downarrow \!{\rm C}_F(X)$ be the family of hypographs of all continuous maps from $X$ to $[0,1]$ endowed with the Fell topology. It is proved that $X$ has a dense separable metrizable locally compact open subset if $\downarrow \!{\rm C}_F(X)$ is metrizable. Moreover, for a first-countable space $X$, $\downarrow \!{\rm C}_F(X)$ is metrizable if and only if $X$ itself is a locally compact separable metrizable space. There exists a Tychonoff space $X$ such that $\downarrow \!{\rm C}_F(X)$ is metrizable but $X$ is not first-countable.
【 授权许可】
CC BY
【 预 览 】
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RO201901232949372ZK.pdf | 83KB | download |