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Two Continua Having A Property of J. L. Kelley

Published online by Cambridge University Press:  20 November 2018

W. T. Ingram  and
D. D. Sherling
W. T. Ingram
Affiliation:
University of Missouri-Rolla, Rolla, Missouri, USA 65401
D. D. Sherling
Affiliation:
Denison University Granville, Ohio, USA 43023
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Abstract

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In proving the contractibility of certain hyperspaces J. L. Kelley identified and defined a certain uniformnessproperty which he called Property 3.2. It is known that the classes of locally connected continua, homogeneous continua and hereditarily indecomposable continua have Property 3.2. In this paper we prove that two examples of indecomposable continua developed respectively by the authors have Property 3.2. One is the example of a nonchainable atriodic tree-like continuum with positive span which was defined by the first author, and the other is a nonchainable, noncircle-like continuum which has the cone=hyperspace property which was defined by the second author. Each of the examples is an inverse limit of an inverse system having a single bonding map.

Keywords

54B2054F15indecomposable continuumhyperspacesproperty k
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 351 - 356
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Ingram, W. T., An atriodic tree-like continuum with positive span, Fund. Math. 77 (1972), 99–107.Google Scholar
2. Kelley, J. L., Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22–36.Google Scholar
3. Nadler, Sam B. Jr., Hyperspaces of Sets. Marcel Dekker, Inc., New York, 1978.Google Scholar
4. Segal, J., Hyperspaces of the inverse limit space, Proc. Amer. Math. Soc. 10 (1959), 706–709.Google Scholar
5. Sherling, D. D., Concerning the cone-hyperspaceproperty, Can. J. Math. 35 (1983), 1030–1048.Google Scholar
6. Wardle, R. W., On a property of J. L. Kelley, Houston J. Math. 3 (1977), 291–299.Google Scholar