Selections, extensions and collectionwise normality |
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Authors: | Valentin Gutev Narcisse Roland Loufouma Makala |
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Affiliation: | School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa |
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Abstract: | We demonstrate that the classical Michael selection theorem for l.s.c. mappings with a collectionwise normal domain can be reduced only to compact-valued mappings modulo Dowker's extension theorem for such spaces. The idea used to achieve this reduction is also applied to get a simple direct proof of that selection theorem of Michael's. Some other possible applications are demonstrated as well. |
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Keywords: | Set-valued mapping Lower semi-continuous Selection Extension |
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