Some results on the extension of single and multivalued maps

In-Sook Kim, Martin Väth

DOI: http://dx.doi.org/10.12775/TMNA.2006.024

Abstract


Necessary and sufficient conditions for single-valued extensions of
multivalued maps are discussed. Moreover, a quantitative version of a
generalization of Dugundji's extension theorem for multivalued maps is
obtained. Finally, the extension problem for compact maps is studied.
Many of the results are new even for single-valued maps.

Keywords


Extension theorem; multi-valued map; upper semicontinuous map; approximation property; retraction; convex map; compact extension

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