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Titlebook: Continuous Selections of Multivalued Mappings; Dušan Repovš,Pavel Vladimirovič Semenov Book 1998 Springer Science+Business Media Dordrecht

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书目名称Continuous Selections of Multivalued Mappings
编辑Dušan Repovš,Pavel Vladimirovič Semenov
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Continuous Selections of Multivalued Mappings;  Dušan Repovš,Pavel Vladimirovič Semenov Book 1998 Springer Science+Business Media Dordrecht
描述This book is dedicated to the theory of continuous selections of multi­ valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as !‘J-n area which has been intensively developing in recent decades and has found various applications in general topology, theory of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point theory, functional and convex analysis, game theory, mathematical economics, and other branches of modern mathematics. The fundamental results in this the­ ory were laid down in the mid 1950‘s by E. Michael. The book consists of (relatively independent) three parts - Part A: Theory, Part B: Results, and Part C: Applications. (We shall refer to these parts simply by their names). The target audience for the first part are students of mathematics (in their senior year or in their first year of graduate school) who wish to get familiar with the foundations of this theory. The goal of the second part is to give a comprehensive survey of the existing results on continuous selections of multivalued mappings. It is intended for specialists in this are
出版日期Book 1998
关键词Dimension; Grad; Homeomorphism; functional analysis; manifold; topology
版次1
doihttps://doi.org/10.1007/978-94-017-1162-3
isbn_softcover978-90-481-5111-0
isbn_ebook978-94-017-1162-3
copyrightSpringer Science+Business Media Dordrecht 1998
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Finite-Dimensional Selection Theoremer 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:
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Examples and Counterexamplesin the main selection theorems of §1–§5. In Theorems (6.1), (6.4), (6.5) and (6.10) we follow (with modifications) [258]. Theorem (6.8) is taken from [271] (for another proof see [79]). Example from Theorem (6.7) was constructed in [262]. The remarkable example due to Pixley [331] is the last theore
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Addendum: New Proof of Finite-Dimensional Selection Theoremed by Ščepin and Brodskiĭ [373]. First, note that there is only one proof of the Finite-dimensional selection theorem [259]. (Observe that the proof [131] is a reformulation of Michael’s proof in terms of coverings and provides a way to avoid . metric considerations.) Second, [373] gives in fact a g
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