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Another Class of Cyclicly Extensible and Reducible Properties

Published online by Cambridge University Press:  20 November 2018

B. Lehman
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 = A ∪ B 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.

Keywords

54F5554F2354F30Cyclic extensibilitycyclic reducibilityunicoherence
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 103 - 106
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Lehman, B., Some conditions related to local connectedness, Duke Math. J., 41 (1974), pp. 247–253.Google Scholar
2. Lehman, B., Cyclic element theory in connected and locally connected Hausdorjf spaces, Can. J. Math 28 (1976), pp. 1032–1050.Google Scholar
3. Lehman, B., K-coherence is cyclicly extensible and reducible, Can. J. Math., 32 (1980), pp. 1270–1276.Google Scholar
4. Vietoris, L., Uber den Hoheren Zusammenhang von Vereinigungsmengen und Durchschnitter, Fund. Math. 19(1932), pp. 265–273.Google Scholar
5. Whyburn, G.T., Analytic Topology. Amer. Math. Soc. Coll. Publ. XXVIII. (1942).Google Scholar
6. Whyburn, G.T., Cut points in general topological spaces, Proc. Nat. Acad. Sci., 61 (1968), pp. 380—387.Google Scholar