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Another Class of Cyclicly Extensible and Reducible Properties

Published online by Cambridge University Press:  20 November 2018

B. Lehman*
Affiliation:
University of GuelphDepartment of Mathematics and Statistics Guelph, Ontario, Canada NIG 2W1
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Abstract

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A space S has property P-1 if S is nonempty. For n > — 1, S has property Pn if it is locally connected, has property Pn-1 and if whenever it is written as a union, S = AB where each of A and B is closed and has property Pn-1, then A ∩ B also has property Pn-1. The purpose of this paper is to establish that for locally compact spaces, each of the properties Pn is both cyclicly extensible and reducible.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

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