Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-28T17:22:32.695Z Has data issue: false hasContentIssue false

Metrization of Ranked Spaces

Published online by Cambridge University Press:  20 November 2018

Fumie Ishikawa*
Affiliation:
Department of Mathematics, Osaka Women's University, Daisen-Cho Sakai City, Osaka 590, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

K. Kunugi introduced the notion of ranked space as a generalization of that of metric spaces, (see [6]). In this note we define a metrizability of ranked spaces and study conditions under which a ranked space is metrizable.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Aleksandrov, P. and Urysohn, P., Une condition nécessaire et suffisante pour qu'une classe (L) soit une classe (D), Comp. Rendus. 177, 1274-1276 (1923).Google Scholar
2. Chittenden, E. W., On the equivalence of écart and voisinage, Trans. Amer. Math. Soc. 18, 161-166 (1917).Google Scholar
3. Frink, A. H., Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43, 133-142 (1937).CrossRefGoogle Scholar
4. Fréchet, M., Sur quelques points du calcul fonctionel, Rend. Cire. Mat. di Palermo 22, 1-74 (1906).CrossRefGoogle Scholar
5. Hausdorfї, F., Grundzüge der Mengenlehre, Leipzig 213. (1914).Google Scholar
6. Kunugi, K., Sur la méthode des espaces rangés I, Proc. Japan Acad. 42, 318-322 (1966).Google Scholar