Continuous approximations of multivalued maps
by
Nikolay Brodskiy
University of Saskatchewan, Canada
Coauthors: Alex Chigogidze, Pavel Semenov

Let L be a countable CW-complex and F\colon X --> Y be upper semicontinuous UV^[L]-valued mapping of a paracompact space X to a complete metric space Y. We prove that if X is a C-space of extension dimension \operatornameed X <= [L], then F admits single-valued graph approximations. For L=Sⁿ our result implies well-known approximation theorem for UV^n-1-valued mappings of n-dimensional spaces. For L={point} our theorem implies a theorem of Ancel on approximations of UV^\infty-valued mappings of C-spaces. Moreover, we show that if all point-images of F are connected, then F admits strong approximations.

Date received: February 28, 2003