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Embedding Smooth Dendroids in Hyperspaces

Published online by Cambridge University Press:  20 November 2018

J. Grispolakis  and
E. D. Tymchatyn
J. Grispolakis
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
E. D. Tymchatyn
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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A continuum will be a connected, compact, metric space. By a mapping we mean a continuous function. By a partially ordered space X we mean a continuum X together with a partial order which is closed when regarded as a subset of X × X. We let 2x (resp. C(X)) denote the hyperspace of closed subsets (resp. subcontinua) of X with the Vietoris topology which coincides with the topology induced by the Hausdorff metric. The hyperspaces 2X and C(X) are arcwise connected metric continua (see [3, Theorem 2.7]). If A ⊂ X we let C(A) denote the subspace of subcontinua of X which lie in A.

If X is a partially ordered space we define two functions L, M : X → 2X by setting for each x ∊ X

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 130 - 138
Copyright
Copyright © Canadian Mathematical Society 1979

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