New Criteria for the Existence of a Continuous ε-Selection
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We study sets admitting a continuous selection of near-best approximations and characterize those sets in Banach spaces for which there exists a continuous ε-selection for each ε > 0. The characterization is given in terms of P-cell-likeness and similar properties. In particular, we show that a closed uniqueness set in a uniformly convex space admits a continuous ε-selection for each ε > 0 if and only if it is B-approximately trivial. We also obtain a fixed point theorem.
Keywordscontinuous ε-selection fixed point
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