Some results on the extension of single- and multivalued maps (Q854521)

Starting from Dugundji's famous extension theorem (any continuous map \(f: A\rightarrow Y\) defined on a closed set \(A\) of a metric space \(X\) with values in a convex subset \(Y\) of a locally convex vector space possesses a continuous extension \(F: X\rightarrow Y\)) the main results of the paper are: existence of single-valued continuous extensions of multivalued upper semicontinuous maps with compact convex values (Section 3) and existence of extensions of continuous compact maps (Section 4).