On controlled extensions of functions |
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Authors: | Jo?e Maleši? Pavel V Semenov |
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Institution: | a Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, P.O. Box 2964, Ljubljana, Slovenia 1001 b Department of Mathematics, Moscow City Pedagogical University, 2nd Selskokhozyastvennyi pr. 4, Moscow, Russia 129226 |
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Abstract: | For any numerical function we give sufficient conditions for resolving the controlled extension problem for a closed subset A of a normal space X. Namely, if the functions , and satisfy the equality E(f(a),g(a))=h(a), for every a∈A, then we are interested to find the extensions f? and ? of f and g, respectively, such that , for every x∈X. We generalize earlier results concerning E(u,v)=u·v by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings. |
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Keywords: | Multivalued mapping Continuous selection Controlled extension Normal space Soft mapping |
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