Approximate and relaxed solutions of differential inclusions
Selections and representations of multifunctions in paracompact spaces
Let (X,T) be a paracompact space, Y a complete metric space, a lower semicontinuous multifunction with nonempty closed values. We prove that if is a (stronger than T) topology on X satisfying a compatibility property, then F admits a -continuous selection. If Y is separable, then there exists a sequence of -continuous selections such that for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets of ℝ × E.
Extensions and selections of maps with decomposable values
Existence results for infinite dimensional differential equations without compactness
A continuous version of Liapunov's convexity theorem
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