$ G $-Metrizable Spaces and the Images of Semi-Metric Spaces
Czechoslovak Mathematical Journal Ying Ge; Shou Lin g-metrizable spaces and the images of semi-metric spaces Czechoslovak Mathematical Journal, Vol. 57 (2007), No. 4, 1141–1149 Persistent URL: http://dml.cz/dmlcz/128231 Terms of use: © Institute of Mathematics AS CR, 2007 Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz Czechoslovak Mathematical Journal, 57 (132) (2007), 1141–1149 g-METRIZABLE SPACES AND THE IMAGES OF SEMI-METRIC SPACES Ying Ge, Jiangsu, Shou Lin, Fujian (Received November 8, 2005) Abstract. In this paper, we prove that a space X is a g-metrizable space if and only if X is a weak-open, π and σ-image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and mssc-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”. Keywords: g-metrizable spaces, sn-metrizable spaces, weak-open mappings, strong sequence-covering mappings, quotient mappings, π-mappings, σ-mappings, mssc-mappings MSC 2000 : 54C10, 54D55, 54E25, 54E35, 54E40 1. Introduction g-metrizable spaces as a generalization of metric spaces have many important properties [17]. To characterize g-metrizable spaces as certain images of metric spaces is an interesting question in the theory of generalized metric spaces, and many “nice” characterizations of g-metrizable spaces have been obtained ([6], [8], [7], [13], [18], [19]).
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