Some Questions on Metrizability
Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 143
Voir la notice de l'article provenant de 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 },
publisher = {mathdoc},
volume = {_N_S_76},
number = {90},
year = {2004},
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/