Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T08:15:50.503Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
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.

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

Aarts, J. M. (1968), Every metric compactification is a Wallman compactification, Proc. Int. Symp. on Topology and its Applications (Herceg-Novi (1968)).Google Scholar
Banaschewski, B. (1963), ‘On Wailman's method of compactification’, Math. Nachr. 27, 105–140.CrossRefGoogle Scholar
Biles, C. M. (1970), ‘Wallman-type compactifications’, Proc. Amer. Math. Soc. 25, 363–368.CrossRefGoogle Scholar
Frink, O. (1964), ‘Compactifications and semi-normal spaces’, Amer. J. Math. 86, 602–707.CrossRefGoogle Scholar
Hamburger, P. (1971), ‘On Wallman-type, regular Wallman-type and Z-compactifications’, Period. Math. Hungar. 1, 303–309.CrossRefGoogle Scholar
Njastad, O. (1966), ‘On Wallman-type compactifications’, Math. Z. 91, 267–276.CrossRefGoogle Scholar
Steiner, E. F. (1968), ‘Wallman spaces and compactifications’, Fund. Math. 61, 295–304.CrossRefGoogle Scholar
Steiner, A. K. and Steiner, E. F. (1968), ‘Products of compact metric spaces are regular Wallman’, Indag. Math. 30, 426–430.Google Scholar
Steiner, A. K. and Steiner, E. F. (1969), ‘On countable multiple point compactifications’, Fund. Math. 65, 133–137.CrossRefGoogle Scholar