Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-22T19:09:47.860Z Has data issue: false hasContentIssue false
  • English
  • Français

Compactness and ordinals

Published online by Cambridge University Press:  18 May 2009

C. J. Knight
C. J. Knight
Affiliation:
The University, Sheffield, 10
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.

If p and q are cardinal numbers and E is a topological space, then the following property may or may not hold:

Every cover of Eby fewer than q open sets has a subcover by fewer than pof them. (1)

Clearly these properties, for various numbers p and q, are far from being independent; in this paper, we investigate some of the interrelationships between them.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 153 - 158
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Alexandroff, P. and Urysohn, P., Mémoire sur les espaces topologiques compacts, Nederl. Akad. Wetensch. Proc. Ser. A 14 (1929), 1–96.Google Scholar
2.Gál, I. S., On a generalised notion of compactness I, Nederl. Akad. Wetensch. Proc. Ser. A 60 (1957), 421–430.CrossRefGoogle Scholar
3.Gál, I. S., On a generalised notion of compactness II, Nederl. Akad. Wetensch. Proc. Ser. A 60 (1957), 431–435.CrossRefGoogle Scholar
4.Gál, I. S., On the theory of (m, n)-compact topological spaces, Pacific J. Math. 8 (1958), 721–734.CrossRefGoogle Scholar
5.Sierpinski, W., Cardinal and ordinal numbers (Warsaw, 1958).Google Scholar