Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T01:08:13.436Z Has data issue: false hasContentIssue false
  • English
  • Français

Metric Spaces Without Large Closed Discrete Sets

Published online by Cambridge University Press:  20 November 2018

W. W. Comfort  and
Anthony W. Hager
W. W. Comfort
Affiliation:
Wesleyan University Middletown, Connecticut
Anthony W. Hager
Affiliation:
Wesleyan University Middletown, Connecticut
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.

We investigate the structure of those non-separable metric spaces X, and their Stone-Čech compactifications, for which X has no closed discrete subspace of power equal to the weight of X. (Throughout this paper we denote the weight of X—the smallest power of a base for the topology of X—by the symbol wX.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 611 - 626
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Atsuji, Masahiko, Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 11–16.Google Scholar
2. Comfort, W. W., An example in density character, Archiv der Math. 14 (1963), 422–423.Google Scholar
3. Comfort, W. W., A survey of cardinal invariants, General Topology and Its Applications 1 (1971), 163–199.Google Scholar
4. Comfort, W. W. and Negrepontis, S., The theory of ultrafilters, Grundlehren der Math. Wissenschaften Band 211 (Springer-Verlag. Heidelberg. 1974).Google Scholar
5. Easton, William B., Powers of regular cardinals, Annals of Math. Logic 1 (1970), 139–178.Google Scholar
6. Engelking, R., Outline of general topology (North-Holland Publishing Co. Amsterdam. 1968).Google Scholar
7. Freiwald, Ronald C., Cardinalities of metric completions, Fundamenta Math. 78 (1973), 275–280.Google Scholar
8. Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (D. Van Nostrand Co., Inc. Princeton, New Jersey. 1960).Google Scholar
9. Haratomi, K., Uber hôherstufige Separabilitdt und Kompaktheit, Jap. J. Math. 8 (1931), 113–141.Google Scholar
10. Rainwater, John, Spaces whose finest uniformity is metric, Pacific J. Math. 9 (1959), 567–570.Google Scholar
11. Karl Schmidt, Friedrich, Ûber die Dichte metrischer Raume, Math. Annalen 106 (1932), 457–472.Google Scholar
12. Stone, A. H., Cardinals of closed sets, Mathematika 6 (1959), 99–107.Google Scholar
13. Urysohn, Paul, Sur un espace métrique universel, Bull, des Sci. Math. 2me Série 51 (1927), 43–64.Google Scholar
14. Willard, Stephen, General topology (Addison-Wesley Publishing Co. Reading, Massachusetts. 1970).Google Scholar