Vertex-facet incidences of unbounded polyhedra.
Joswig, Michael, Kaibel, Volker, Pfetsch, Marc E., Ziegler, Günter M. (2001)
Advances in Geometry
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Joswig, Michael, Kaibel, Volker, Pfetsch, Marc E., Ziegler, Günter M. (2001)
Advances in Geometry
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Buba-Brzozowa, Malgorzata (2000)
Journal for Geometry and Graphics
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Wilfrid Wilson (1937)
Compositio Mathematica
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Tadeusz Januszkiewicz, Jacek Świątkowski (2006)
Publications Mathématiques de l'IHÉS
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We introduce a family of conditions on a simplicial complex that we call local -largeness (≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as...
Bacher, R., Krattenthaler, C. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Burgiel, H., Reiner, V. (1998)
The New York Journal of Mathematics [electronic only]
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Koźniewski, Edwin, Górska, Renata A. (2000)
Journal for Geometry and Graphics
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Adam Idzik, Konstanty Junosza-Szaniawski (2005)
Discussiones Mathematicae Graph Theory
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We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.
W. Dębski (1990)
Colloquium Mathematicae
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Athanasiadis, Christos A. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Milica Stojanović (2005)
Matematički Vesnik
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Karol Pąk (2011)
Formalized Mathematics
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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....
Lee, Carl W. (2011)
The Electronic Journal of Combinatorics [electronic only]
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