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  3. Formalized Mathematics
  4. Formalized Mathematics, 2011, Volume 19, Issue 3

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3610
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    Pole DCWartośćJęzyk
    dc.contributor.authorPąk, Karol-
    dc.date.accessioned2015-12-06T19:04:50Z-
    dc.date.available2015-12-06T19:04:50Z-
    dc.date.issued2011-
    dc.identifier.citationFormalized Mathematics, Volume 19, Issue 3, 2011, Pages 145-150-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3610-
    dc.description.abstractIn this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the notion of a bounded simplicial complex and the diameter of a bounded simplicial complex. We also prove the estimation of diameter decrease which is connected with the barycentric subdivision. Finally, we prove the Brouwer fixed point theorem and compute the small inductive dimension of εn. This article is based on [16].-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleBrouwer Fixed Point Theorem for Simplexes-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-011-0023-4-
    dc.description.AffiliationInstitute of Informatics, University of Białystok, Poland-
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    dc.description.referencesKarol Pąk. Small inductive dimension of topological spaces. Formalized Mathematics, 17(3):207-212, 2009, doi: 10.2478/v10037-009-0025-7.-
    dc.description.referencesKarol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.-
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    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2011, Volume 19, Issue 3

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