Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T15:04:00.759Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum zero-dimensional compactifications

Published online by Cambridge University Press:  24 October 2008

J. R. McCartney
J. R. McCartney
Affiliation:
University of Glasgow
Get access Rights & Permissions [Opens in a new window]

Extract

All spaces considered in this paper are Hausdorff. θX is a compactification of a completely regular space X means that X is identified with a dense subspace of θX. We shall thus always regard X to be contained in θX. A compactification θX of X is zero-dimension (countable) if its ‘outgrowth” θX ~ X is zero-dimensional (countable).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 653 - 661
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Aleksandrov, S.On some basic directions in general topology. Russian Math. Surveys, 19 (6) (12. 1964), 1–40.CrossRefGoogle Scholar
(2)Bourbaki, N.Elements of mathematics, general topology (Addison Wesley, 1966).Google Scholar
(3)Engelking, R. and Sklyarenko, E. G.On compactifications allowing extensions of mappings. Fund. Math. 53 (1963), 65–79.CrossRefGoogle Scholar
(4)Freudenthal, H.Neuaufbau der Endentheorie. Ann. of Math. 43 (2) (1942), 261–279.CrossRefGoogle Scholar
(5)Gillman, L. and Jerison, M.Rings of continuous functions (Van Nostrand, 1960).CrossRefGoogle Scholar
(6)Henriksen, M. and Isbell, J. R.Local connectedness in the Stone–Cech compactification. Illinois J. Math. 1 (1957), 574–582.CrossRefGoogle Scholar
(7)Isbell, J. R.Uniform spaces. Amer. Math. Soc., Math. Surveys No. 12 (1964).CrossRefGoogle Scholar
(8)Magill, K. D.N-point compactifications. Amer. Math. Monthly 72 (1965), 1075–1081.CrossRefGoogle Scholar
(9)Ponomarev, V. I.Mat. Sb. 48 (90) (1959), 191–212 (in Russian).Google Scholar
(10)Pospisil, B.Remarks on bicompact spaces. Ann. of Math. 38 (1937), 845–846.CrossRefGoogle Scholar
(11)Sklyarenko, E. G.On perfect bicompact extensions. Soviet Math. Dokl. 2 (1961), 238–240.Google Scholar
(12)Sklyarenko, E. G.Perfect bicompact extensions. Soviet Math. Dokl. 3 (1962), 1455–1458.Google Scholar
(13)Sklyarenko, E. G.Isv. Akad. Nauk SSSR, Ser. Mat. 26 (1962), 427–453 (in Russian).Google Scholar
(14)Steiner, A. K. and Steiner, E. F.Wallman and Z-compactifications. Duke Math. J. 35 (1968), 269–275.CrossRefGoogle Scholar