Some Properties of Hyperspaces with Applications to Continua Theory

Grispolakis, J. ; Jr., Sam B. Nadler ; Tymchatyn, E. D.

Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 197-210

Résumé

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 chainableIn [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].

Détail

DOI : 10.4153/CJM-1979-021-9

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