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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Continuity of additive $ \kappa$-metric functions and metrization of $ \kappa$-metric spaces


Author: Takesi Isiwata
Journal: Proc. Amer. Math. Soc. 104 (1988), 988-992
MSC: Primary 54E35; Secondary 54C05, 54E15, 54E99
MathSciNet review: 964884
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Abstract: For an additive $ \kappa$-metric space $ X$ with an $ s\left( x \right)$-continuous $ \kappa $-metric $ d\left( {x,C} \right)$, we prove that $ X$ is metrizable, and that if $ d\left( {x,C} \right)$ is locally regular, then $ z\left( {x,y} \right)$ is bicontinuous, and $ \rho \left( {x,y} \right) = z\left( {x,y} \right) + z\left( {x,y} \right)$ is a metric on $ X$ which agrees with the topology of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0964884-5
PII: S 0002-9939(1988)0964884-5
Keywords: Metrization, additive $ \kappa $-metric, Vietoris topology, continuous maps
Article copyright: © Copyright 1988 American Mathematical Society