Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T03:55:43.994Z Has data issue: false hasContentIssue false
  • English
  • Français

Derived Subspaces of Metric Spaces

Published online by Cambridge University Press:  20 November 2018

Harold W. Martin
Harold W. Martin*
Affiliation:
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Rights & Permissions [Opens in a new window]

Extract

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.

It is shown that the boundary of the set of accumulation points of a metrizable space X is compact iff X has a compatible metric d such that d(A, B)>0 whenever A and B are disjoint closed subsets of X, each of which is disjoint from the set of accumulation points.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 465 - 467
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Alster, K., Metric spaces all of whose decompositions are metric, Bui Polon. ScL, 20 (1972), 395-400.Google Scholar
2. Atsuji, M., Uniform continuity of continuous functions of metric spaces, Pacific J. Math., 8 (1958), 11-16.Google Scholar
3. Aull, C. E., Closed set countability axioms, Indag. Math., 28 (1966), 311-316.Google Scholar
4. Ginsburg, J., The metrizability of spaces whose diagonals have a countable base, Canad. Math. Bull, 20 (1977), 513-514.Google Scholar
5. Nagata, J., On the uniform topology of bicompactifications, J. Inst. Polytech. Osaka City Univ., 1 (1950), 28-39.Google Scholar
6. Rainwater, J., Spaces whose finest uniformity is metric, Pacific J. Math., 9 (1959), 567-570.Google Scholar
7. Willard, S., Metric spaces all of whose decompositions are metric, Proc. Amer. Math. Soc, 21 (1969), 126-128.Google Scholar