Densely two-valued metric projections in uniformly convex Banach spaces |
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Authors: | N. V. Zhivkov |
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Affiliation: | (1) Institute of Mathematics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria |
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Abstract: | For every uniformly convex Banach spaceX with dimX 2 there is a residual setU in the Hausdorff metric spaceB(X) of bounded and closed sets inX such that the metric projection generated by a set fromU is two-valued and upper semicontinuous on a dense and everywhere continual subset ofX. For any two closed and separated subsetsM1 andM2 ofX the points on the equidistant hypersurface which have best approximations both inM1 andM2 form a dense G set in the induced topology.The author is partially supported by the National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under contract MM 408/94. |
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Keywords: | Primary 41A65, 54E52 Secondary 46B20 |
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