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Wallman compactifications and Wallman realcompactifications

Published online by Cambridge University Press:  09 April 2009

M. S. Gagrat  and
S. A. Naimpally
M. S. Gagrat
Affiliation:
Mathematics DepartmentIndian Institute of Technology, Kanpur Kanpur–16, U.P. India
S. A. Naimpally
Affiliation:
Mathematics DepartmentIndian Institute of Technology, Kanpur Kanpur–16, U.P. India
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In 1964 Frink [8] generalized Wallman's method [17] of compactification and asked the question: “Is every Hausdorff compactification of a Tychonoff space a Wallman compactification?”. This problem, which is as yet unsolved, has led to the discovery of a number of necessary and/or sufficient conditions for a Hausdorff compactification to be Wallman; (see Alò and Shapiro [2], [3], Banasĉhewski [6], Njåstad [13] and Steiner [15]). Recently Alò and Shapiro [4], [5] have generalized the Wallman procedure to discuss what they call Z*-realcompact spaces and Z*-realcompactification n(Z) corresponding to a countably productive (c.p.) normal base Z on X. Some further work has been done by Steiner and Steiner [14].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 4 , June 1973 , pp. 417 - 427
Copyright
Copyright © Australian Mathematical Society 1973

References

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