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Some Properties of Hyperspaces with Applications to Continua Theory

Published online by Cambridge University Press:  20 November 2018

J. Grispolakis ,
Sam B. Nadler Jr.  and
E. D. Tymchatyn
J. Grispolakis
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
Sam B. Nadler Jr.
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
E. D. Tymchatyn
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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In 1972, Lelek introduced the notion of Class (W) in his seminar at the University of Houston [see below for definitions of concepts mentioned here]. Since then there has been much interest in classifying and characterizing continua in Class (W). For example, Cook has a result [5, Theorem 4] which implies that any hereditarily indecomposible continuum is in Class (W) Read [21, Theorem 4] showed that all chainable continua are in Class (W), and Feuerbacher proved the following result:

(1.1) THEOREM [7, Theorem 7]. A non-chainable circle-like continuum is in Class (W) if and only if it is not weakly chainable

In [14, 4.2 and section 6], a covering property (denoted here and in [18] by CP) was defined and studied primarily for the purpose of proving that indecomposability is a Whitney property for the class of chainable continua [14, 4.3].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 197 - 210
Copyright
Copyright © Canadian Mathematical Society 1979

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