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Local Topological Properties and One Point Extensions

Published online by Cambridge University Press:  20 November 2018

John Mack ,
Marlon Rayburn  and
Grant Woods
John Mack
Affiliation:
University of Kentucky, Lexington, Kentucky
Marlon Rayburn
Affiliation:
University of Kentucky, Lexington, Kentucky
Grant Woods
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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In 1957, Mrowka [12] showed that a locally paracompact space admits a one point paracompactification (see also [2, Chapter 9, § 4, Exercise 27]). Similarly, in [9] Isiwata obtained a one point realcompactincation for locally realcompact spaces. Recently a number of authors (see [11, 16; 17; 18; 21]) have constructed one point P-extensions of local P-spaces for a variety of topological properties P. It is the purpose of this paper to draw together the various techniques used by the above mentioned authors and to study the set (lattice) of all one point P-extensions of a particular space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 2 , April 1972 , pp. 338 - 348
Copyright
Copyright © Canadian Mathematical Society 1972

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