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Multiple points and Wallman compactifications

Published online by Cambridge University Press:  09 April 2009

Olav Njastad
Olav Njastad
Affiliation:
University of ColoradoBoulder, U.S.A.
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Banaschewski (1963) and Frink (1964) generalized the compactification procedure of Wallman to obtain Hausdorff compactifications of Tychonoff spaces. Numerous papers have been devoted to the problem whether all Hausdorff compactifications may be obtained in this way, and for many classes of compactifications an affirmative answer has been given. This note is a contribution in this direction. We show that if a (Hausdorff) compactification αX of X is the quotient space of a Wallman compactification γX in such a way that the set of multiple points of αX with respect to γX is not too large, then αX too is a Wallman compactification. The results are generalizations of earlier results of Steiner and Steiner (1968) and by the author (1966) for the special case that γX is the Stone Čech-compactification.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 274 - 280
Copyright
Copyright © Australian Mathematical Society 1975

References

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