منابع مشابه
Extending Generalized Whitney Maps
For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
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It is shown that there is no Whitney map on the hyperspace 2x for nonmetrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X). Given a Hausdorff compact space X, we consider the space 2x of all non-empty compact subsets of X equipped with the Vietoris topology. Any subspace H (X) of the space 2x is ...
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We obtain generalizations of the Fan’s matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.
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V. GRADINARU AND R. HIPTMAIR † Abstract. Conforming finite elements inH(div; Ω) andH(curl; Ω) can be regarded as discrete differential forms (Whitney–forms). The construction of such forms is based on an interpolation idea, which boils down to a simple extension of the differential form to the interior of elements. This flexible approach can accommodate elements of more complicated shapes than ...
متن کاملFixed Point Theory for Admissible Type Maps with Applications
In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1988
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-56-2-299-309