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.
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 193–204, 1975.
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Koshcheev, V.A. The connectivity and approximative properties of sets in linear normed spaces. Mathematical Notes of the Academy of Sciences of the USSR 17, 114–119 (1975). https://doi.org/10.1007/BF01161866
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DOI: https://doi.org/10.1007/BF01161866