The connectivity and approximative properties of sets in linear normed spaces

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Abstract

The connectivity of suns is investigated. It is shown that a sun is connected in finite-dimensional space. A set M in uniformly convex space X is shown to be approximatively compact if and only if M is P-compact and the metric projection of X onto M is upper semicontinuous. © 1975 Plenum Publishing Corporation.

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Koshcheev, V. A. (1975). The connectivity and approximative properties of sets in linear normed spaces. Mathematical Notes of the Academy of Sciences of the USSR, 17(2), 114–119. https://doi.org/10.1007/BF01161866

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