Geodesic
Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces
Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 268-282 Cet article a éte moissonné depuis la source Math-Net.Ru

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Generalized $n$-piecewise functions constructed from given monotone path-connected boundedly compact subsets of the space $C[a,b]$ are studied. They are shown to be monotone path-connected suns. In finite-dimensional polyhedral spaces, luminosity points of sets admitting a lower semicontinuous selection of the metric projection operator are investigated. An example of a non-$B$-connected sun in a four-dimensional polyhedral normed space is constructed. Bibliography: 14 titles.
Keywords: monotone path-connected set, Menger-connectedness, stably monotone path-connectedness, sun. 
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I. G. Tsar'kov. Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces. Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 268-282. http://geodesic.mathdoc.fr/item/SM_2022_213_2_a5/

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