Gleason-score
发表于 2025-3-23 12:47:49
Selection Theorems for Nonconvex-Valued Mapsr, in that example the family {.(.)}, . ∈ ., was not an ELC.-family of subsets of the Euclidean plane. A more sophisticated example of Pixley (see ., §6) shows that for an infinite-dimensional domain (namely, for the Hilbert cube .) it is possible to find a lower semicontinuous map . with {.(.)}, .
Mnemonics
发表于 2025-3-23 16:53:23
Miscellaneous Resultsany selection problem is purely a topological question. However, all known solutions of selection problems use a suitable metric structure of the range of the multivalued mapping, i.e. “metric” proofs yield “topological” answers. So, a very natural question arises: .
promote
发表于 2025-3-23 20:39:36
Measurable Selectionse modern point of view such a problem evidently is a special case of a selection problem: find a selection of multivalued mapping . ↦ {y ∈ . | .(., .) = 0}. This problem was originally started without using any “selection” terms and goes back to Hadamard and Lusin.
Banquet
发表于 2025-3-23 22:47:12
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温顺
发表于 2025-3-24 03:28:50
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Tracheotomy
发表于 2025-3-24 07:11:28
Homeomorphism Group Problemmple, the Banach space of continuous functions on the cube .., the space of diffeomorphisms of the sphere .., etc. Among such examples, the groups .(.) of all self-homeomorphisms of an .-dimensional compact manifolds stand at the top. An intensive study of .(.) started in the mid 1950’s, accordingly
rectocele
发表于 2025-3-24 14:36:02
Dirk Berg-Schlosser,Ferdinand Müller-Rommelof of Convex-valued theorem, but without any partitions of unity. As in the previous paragraph we begin (see Section 1) by the necessity conditions for solvability of the selection problem for an arbitrary closed-valued mapping. Our proof of Theorem (2.4) follows the original one . The converse theorem (2.1) is a well-known folklore result.
泄露
发表于 2025-3-24 18:18:53
Vergleichende Wertewandelforschunger semicontinuous mapping. The aim of the present chapter is to find a solution for at most (. + 1)-dimensional paracompact domains, . ∈ {−1, 0, 1, 2,...}. More precisely, we shall give an answer to the following question:
是贪求
发表于 2025-3-24 20:59:05
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Conserve
发表于 2025-3-25 02:53:03
https://doi.org/10.1007/978-3-322-86943-2e, one can start by arbitrary continuous singlevalued map . : .→. and then define .(.) to be a subset of . such that . (.) ∈ .(.). Then . is a continuous selection for ., but there are no continuity type restrictions for ..