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Domains of Paracompactness and Local Compactness

Published online by Cambridge University Press:  20 November 2018

Brian Warrack
Brian Warrack*
Affiliation:
School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario
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Given a class of topological spaces and a class of mappings of topological spaces, the -résolvant of is denned to be the class of topological spaces all of whose -images lie in . Whenever is closed under composition and includes identity maps, is easily seen to be the largest class of spaces smaller than which is closed under -images.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 449 - 454
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. MacDonald, S. and Willard, S., Domains of paracompactness and regularity, Can. J. Math. 24 (1972), 1079–1085.Google Scholar
2. Mori ta, K., On spaces having the weak topology with respect to closed coverings. II, Proc. Japan Acad. 30 (1954), 711–717.Google Scholar
3. Warrack, B., Regular quotients of metric spaces, Can. Math. Bull. 18 (1975), 611–613.Google Scholar