Hostname: page-component-7bb8b95d7b-wpx69 Total loading time: 0 Render date: 2024-09-18T02:54:35.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Ordered compactifications with countable remainders

Published online by Cambridge University Press:  17 April 2009

D.C. Kent  and
T.A. Richmond
D.C. Kent
Affiliation:
Department of Pure and Applied Mathematics WashingtonState University Pullman, WA 99164–3113United States of America
T.A. Richmond
Affiliation:
Department of Mathematics Western KentuckyUniversity Bowling Green, KY 42101United States of America
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.

It is shown that if a partially-ordered topological space X admits a finite-point T2-ordered compactification, then it admits a countable T2-ordered compactification if and only if it admits n−point T2-ordered compactifications for all n beyond some integer m.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 483 - 488
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Cain, G.L., ‘Countable compactifications’, in General topology and its ralations to modern analysis and algebra VI, (Frolík, Z., Editor), Proc. Sixth Prague Topological Symposium 1986 (Heldermann Verlag, Berlin, 1988), pp. 69–75.Google Scholar
[2]Chandler, R.E., Hausdorff compactifications, Lecture Notes in Pure and Appl. Math. 23 (Marcel Dekker, Inc., New York, 1976).Google Scholar
[3]Engelking, R. and Sklyarenko, E.G., ‘On compactifications allowing extensions of mappings’, Fund. Math. 53 (1963), 65–79.CrossRefGoogle Scholar
[4]Fletcher, P. and Lindgren, W., Quasi-uniform spaces, Lecture Notes in Pure and Appl. Math. 77 (Marcel Dekker, Inc., New York, 1982).Google Scholar
[5]Kimura, T., ‘ℵo-point compactifications of locally compact spaces and product spaces’, Proc. Amer. Math. Soc. 93 (1985), 164–168.Google Scholar
[6]Magill, K.D. Jr., ‘N−point compactifications’, Amer. Math. Monthly 72 (1965), 1075–1081.CrossRefGoogle Scholar
[7]Magill, K.D., ‘Countable compactifications’, Canad. J. Math. 18 (1966), 616–620.CrossRefGoogle Scholar
[8]McCartney, J.R., ‘Maximum zero-dimensional compactifications’, Math. Proc. Cambridge Philos. Soc. 68 (1970), 653–661.CrossRefGoogle Scholar
[9]McCartney, J.R., ‘Maximum countable compactifications of locally compact spaces’, Proc. London Math. Soc. (3) 22 (1971), 369–384.Google Scholar
[10]Nachbin, L., Topology and order, New York Math. Studies 4 (Van Nostrand, Princeton, N.J., 1965).Google Scholar
[11]Richmond, T.A., ‘Finite-point order compactifications’, Math. Proc. Cambridge Philos. Soc. 102 (1987), 467–473.CrossRefGoogle Scholar
[12]Richmond, T.A., ‘Posets of ordered compactifications’, Bull. Austral. Math. Soc. 47 (1993), 59–72.CrossRefGoogle Scholar