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Characterizing Continua by Disconnection Properties

Published online by Cambridge University Press:  20 November 2018

E. D. Tymchatyn  and
Chang-Cheng Yang
E. D. Tymchatyn
Affiliation:
Department of Mathematics, MacLean Hall #142, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, email: tymchatyn@math.usask.ca
Chang-Cheng Yang
Affiliation:
Department of Mathematics, University of Electronic Science & Technology of China, Chengdu, Sichuan 610054, China, email: yangc@math.usask.ca
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Abstract

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We study Hausdorff continua in which every set of certain cardinality contains a subset which disconnects the space. We show that such continua are rim-finite. We give characterizations of this class among metric continua. As an application of our methods, we show that continua in which each countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.

Keywords

54D0554F2054F50disconnection propertiesrim-finite continuagraphs
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 348 - 358
Copyright
Copyright © Canadian Mathematical Society 1998

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