A combinatorial characterization of planar 2-complexes
Jonathan L. Gross, Ronald H. Rosen (1981)
Colloquium Mathematicae
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Displaying similar documents to “On the imbedding of systems of compacta in simplicial complexes”
A combinatorial characterization of planar 2-complexes
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In 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....
A note on intersections of simplices
David A. Edwards, Ondřej F. K. Kalenda, Jiří Spurný (2011)
Bulletin de la Société Mathématique de France
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We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.