منابع مشابه
Selections on Ψ - spaces
We show that if A is an uncountable AD (almost disjoint) family of subsets of ω then the space Ψ(A) does not admit a continuous selection; moreover, if A is maximal then Ψ(A) does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.
متن کاملSelections and Finite C - Spaces
Characterizations of paracompact finite C-spaces via continuous selections avoiding Zσ-sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite C-spaces are also proved.
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Following results of Bourgain and Gorelik we show that the spaces lp, 1 < p < ∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0, then it is isomorphic to c0. We show also that there are B...
متن کاملContinuous Selections and Approximations in Α-convex Metric Spaces
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
متن کاملLipschitz selections of the diametric completion mapping in Minkowski spaces
We develop a constructive completion method in general Minkowski spaces, which successfully extends a completion procedure due to Bückner in twoand three-dimensional Euclidean spaces. We prove that this generalized Bückner completion is locally Lipschitz continuous, thus solving the problem of finding a continuous selection of the diametric completion mapping in finite dimensional normed spaces...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2010
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.06.016