Continuity of additive $\kappa$-metric functions and metrization of $\kappa$-metric spaces
HTML articles powered by AMS MathViewer
- by Takesi Isiwata PDF
- Proc. Amer. Math. Soc. 104 (1988), 988-992 Request permission
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 $X$.References
- Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982, DOI 10.2140/pjm.1966.17.1 A. N. Dranišnikov, Simultaneous annihilator of families of closed sets, $\kappa$-metrizable and stratifiable spaces, Soviet Math. Dokl. 19 (1978), 1466-1469.
- Takesi Isiwata, Metrization of additive $\kappa$-metric spaces, Proc. Amer. Math. Soc. 100 (1987), no. 1, 164–168. MR 883422, DOI 10.1090/S0002-9939-1987-0883422-8
- E. V. Ščepin, Topology of limit spaces with uncountable inverse spectra, Uspehi Mat. Nauk 31 (1976), no. 5 (191), 191–226 (Russian). MR 0464137 —, On $\kappa$-metrizable spaces, Math. USSR Izv. 14 (1980), 407-440. J. Suzuki, K. Tamamo and Y. Tanaka, $\kappa$-metrizable spaces, stratifiable spaces and metrizations, Proc. Amer. Math. Soc.
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 988-992
- MSC: Primary 54E35; Secondary 54C05, 54E15, 54E99
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964884-5
- MathSciNet review: 964884