Vol. 65, No. 1, 1976

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On certain g-first countable spaces

Kyung Bai Lee

Vol. 65 (1976), No. 1, 113–118

In this paper strongly o-metrizable spaces are introduced and it is shown that a space is strongly o-metrizable if and only if it is semistratifiable and o-metrizable (or symmetrizable); g-metrizable spaces are strongly o-metrizable and hence quotient π-images of metric spaces. As what F. Siwiec did for (second countable, metrizable and first countable) spaces, we introduce g-developable spaces, and it is proved that a Hausdorff space is g-developable if and only if it is symmetrizable by a symmetric under which all convergent sequences are Cauchy.

Mathematical Subject Classification 2000
Primary: 54E25
Received: 18 September 1975
Revised: 6 February 1976
Published: 1 July 1976
Kyung Bai Lee