Some Questions on Metrizability
Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 143
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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.
Classification :
54D50 54E35
Keywords: strongly decreasing g-function, CF-family, metrizable space, k-space
Keywords: strongly decreasing g-function, CF-family, metrizable space, k-space
@article{PIM_2004_N_S_76_90_a13,
author = {Ying Ge and Jian-Hua Shen},
title = {Some {Questions} on {Metrizability}},
journal = {Publications de l'Institut Math\'ematique},
pages = {143 },
year = {2004},
volume = {_N_S_76},
number = {90},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2004_N_S_76_90_a13/}
}
Ying Ge; Jian-Hua Shen. Some Questions on Metrizability. Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 143 . http://geodesic.mathdoc.fr/item/PIM_2004_N_S_76_90_a13/