V. Indumathi, N. Hari Prakash
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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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.
Key concepts: Mathematics, Continuous functions on a compact Hausdorff space, Hausdorff space, Subspace topology, Hausdorff distance, Banach space, Metric space, Uniform continuity