Local Uniform Strong Proximinality of the Space of Continuous Vector-Valued Functions |
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| Authors: | V Indumathi N Prakash |
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| Institution: | 1. Department of Mathematics, Pondicherry University, Pondicherry, Indiapdyindumath@gmail.com;3. Department of Mathematics, Pondicherry University, Pondicherry, India |
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| Abstract: | Let X be a Banach space, S be a compact Hausdorff space and Y be a U-proximinal subspace of X. We prove that C(S,Y) is locally uniformly strongly proximinal in C(S,X) and the corresponding metric projection map is Hausdorff metric continuous. |
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| Keywords: | 1 ½-ball property Hausdorff metric continuous metric projection proximinal strongly proximinal U-proximinal |
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