Conditions Which Imply Metrizability in some Generalized Metric Spaces*

A.M. Mohamad


In this paper we show that two important generalized metric properties are generalizations of first countability. We give some conditions on these generalized metric properties which imply metrizability. We prove that, a space $X$ is metrizable if and only if $X$ is a strongly quasi-N-space, quasi$-gamma-$space; a quasi$-gamma$ space is metrizable if and only if it is a pseudo $wN-$ space or quasi$-$Nagata$-$space with quasi $G^*_gamma-$diagonal; a space $X$ is a metrizable space if and only if $X$ has a $CWBC-$map $g$ satisfying the following conditions:
1. $g$ is a pseudo-strongly-quasi-N-map;
2. for any $A subseteq X, overline{A} subseteq cup {g(n, x) : x in A}$.

Nagata space; $gamma-$ Space; metrizable; quasi$-G^*_gamma-$diagonal; first countable.

Math Review Classification
Primary AMS (1991) Subject Classification: 54E30, 54E35.

Last Updated
8 September 1999

17 pages

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