PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 76(90), pp. 143–147 (2004) 

SOME QUESTIONS ON METRIZABILITYYing Ge and JianHua ShenDepartment of Mathematics, Suzhou University, Suzhou 215006, P.R. China and Department of Mathematics, Suzhou Science and Technology College, Suzhou, Jiangsu, 215009, P. R. China.Abstract: Let us say that a $g$function $g(n,x)$ on a space $X$ satisfies the condition ($*$) provided: If $\{x_n\}\to p\in X$ and $x_n\in g(n,y_n)$ for every $n\in N$, then $y_n\to p$. We prove that a $k$space $X$ is a metrizable space (a metrizable space with property $ACF$) if and only if there exists a strongly decreasing $g$function $g(n,x)$ on $X$ such that $\{\overline{g(n,x)}:x\in X\}$ is $CF$ ($\{g(n,x):x\in X\}$ is $CF^*$) in $X$ for every $n\in N$ and the condition ($*$) is satisfied. Our results give a partial answer to a question posed by Z. Yun, X. Yang and Y. Ge and a positive answer to a conjecture posed by S. Lin, respectively. Keywords: strongly decreasing $g$function, $CF$family, metrizable space, $k$space Classification (MSC2000): 54D50; 54E35 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 17 Dec 2004. This page was last modified: 9 Feb 2005.
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