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A Note on Whitney Maps

Published online by Cambridge University Press:  20 November 2018

L. E. Ward Jr.
L. E. Ward Jr.*
Affiliation:
Department of Mathematics University of Oregon Eugene, Oregon 97403 U.S.A.
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In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.

A partially ordered space is a topological space X endowed with a partial order ≤ whose graph is a closed subset of X×X. It is well-known (see, for example, [2], page 167) that if X is a regular Hausdorff space then 2X is a partially ordered space with respect to inclusion.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 373 - 374
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Carruth, J.H., A note on partially ordered compacta. Pacific J. Math., 24 (1968), 229-231.Google Scholar
2. Kuratowski, K., Topology I, Academic Press, New York and London, 1966.Google Scholar
3. Nadler, S.B. Jr., Hyperspaces of sets, Marcel Dekker, New York and Basel, 1978.Google Scholar
4. Ward, L. E. Jr., Partially ordered topological spaces, Proc. Amer. Math. Soc, 5 (1954), 144-161.Google Scholar