Michael's problem and weakly infinite-dimensional spaces |
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Authors: | Alex Karassev |
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Institution: | Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, PO Box 5002, North Bay, ON P1B 8L7, Canada |
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Abstract: | Let X be a compact Hausdorff space. Suppose that any multivalued map , where Y is a Gδ subset of a Banach space, such that the values of F are convex and closed in Y, has a continuous single-valued selection. Then we prove that X is weakly infinite-dimensional. This provides a partial solution of Gδ-problem, posed by Ernest Michael. |
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Keywords: | primary 54C65 secondary 54F45 46B25 28B20 |
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