Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-13T02:26:52.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-point order compactifications

Published online by Cambridge University Press:  24 October 2008

Thomas A. Richmond
Thomas A. Richmond
Affiliation:
Western Kentucky University, Bowling Green, Kentucky 42101, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

After the characterization of 1-point topological compactifications by Alexandroff in 1924, n-point topological compactifications by Magill [4] in 1965, and 1-point order compactifications by McCallion [5] in 1971, spaces that admit an n -point order compactification are characterized in Section 2. If X* and X** are finite-point order compactifications of X, sup{X*, X**} is given explicitly in terms of X* and X** in § 3. In § 4 it is shown that if an ordered topological space X has an m-point and an n-point order compactification, then X has a k-point order compactification for each integer k between m and n. The author is indebted to Professor Darrell C. Kent, who provided assistance and encouragement during the preparation of this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 467 - 473
Copyright
Copyright © Cambridge Philosophical Society 1987

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]Blatter, J.. Order compactifications of totally ordered topological spaces. J. Approx. Theory 13 (1975), 56–65.CrossRefGoogle Scholar
[2]Chandler, R. E.. Hausdorff Compactifications. Lecture Notes in Pure and Appl. Math., Volume 23 (Marcel Dekker, Inc., 1976).Google Scholar
[3]Firby, P. A.. Finiteness at infinity. Proc. Edinburgh Math. Soc. 17 (1971), 299–304.CrossRefGoogle Scholar
[4]Magill, K. D. JrN-point compactifications. Amer. Math. Monthly 72 (1965), 1075–1081.CrossRefGoogle Scholar
[5]McCallion, T.. Compactifications of ordered topological spaces. Proc. Cambridge Philos. Soc. 71 (1972), 463–473.CrossRefGoogle Scholar
[6]McCartan, S. D.. Separation axioms for topological ordered spaces. Proc. Cambridge Philos.Soc. 64 (1968), 965–973.CrossRefGoogle Scholar
[7]Nachbin, L.. Topology and Order. New York Math. Studies, 4 (Van Nostrand, 1965).Google Scholar
[8]Richmond, T. A.. Finite-Point Order Compactifications. Ph.D. Thesis, Washington State University (1986).Google Scholar