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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.
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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

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References

REFERENCES

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