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• W3099133775 abstract "A boundedly compact (boundedly weakly compact) m-connected (Menger-connected) set is shown to be monotone path-allowbreak connected and is a sun in a broad class of Banach spaces (in particular, in separable spaces). Further, the intersection of a boundedly compact monotone path-allowbreak connected (m-connected) set with a closed ball is established to be cell-like (trivial shape) and, in particular, acyclic (contractible, in the finite-dimensional case) and a sun. Further, a boundedly weakly compact m-connected set is asserted to be monotone path-allowbreak connected. In passing, Rainwater--allowbreak Simons's theorem on weak convergence of sequences is extended to the convergence with respect to the associated norm (in the sense of Brown)." @default.
• W3099133775 created "2020-11-23" @default.
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• W3099133775 date "2014-08-27" @default.
• W3099133775 modified "2023-10-16" @default.
• W3099133775 title "Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces" @default.
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• W3099133775 doi "https://doi.org/10.1070/im2014v078n04abeh002702" @default.
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