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On Countably Paracompact Spaces

Published online by Cambridge University Press:  20 November 2018

C. H. Dowker
C. H. Dowker*
Affiliation:
Harvard University
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Let X be a topological space, that is, a space with open sets such that the union of any collection of open sets is open and the intersection of any finite number of open sets is open. A covering of X is a collection of open sets whose union is X. The covering is called countable if it consists of a countable collection of open sets or finite if it consists of a finite collection of open sets ; it is called locally finite if every point of X is contained in some open set which meets only a finite number of sets of the covering. A covering is called a refinement of a covering U if every open set of X is contained in some open set of . The space X is called countably paracompact if every countable covering has a locally finite refinement.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 219 - 224
Copyright
Copyright © Canadian Mathematical Society 1951

References

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