Extending Whitney maps
L. E. Ward · Pacific Journal of Mathematics · 1981
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 2 Σ , 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., 2 X ) can be extended to a Whitney map for C(Y) (resp., 2 F ).The proofs entail recasting these problems in the more inclusive setting of partially ordered spaces and then employing results of Nachbin.