Vol. 93, No. 2, 1981

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Extending Whitney maps

L. E. Ward

Vol. 93 (1981), No. 2, 465–469
Abstract

The following theorems are proved, (1) If X is a continuum then any Whitney map for C(X), the space of subcontinua of X, can be extended to a Whitney map for 2X, the space of nonempty closed subsets of X. (2) If Y is a continuum and X is a subcontinuum of Y then any Whitney map for C(X) (resp., 2X) can be extended to a Whitney map for C(Y ) (resp., 2Y ). The proofs entail recasting these problems in the more inclusive setting of partially ordered spaces and then employing results of Nachbin.

Mathematical Subject Classification 2000
Primary: 54B20
Secondary: 54C20
Milestones
Received: 17 September 1979
Published: 1 April 1981
Authors
L. E. Ward