The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Combinatorial lemmas for polyhedrons I”

Simplicial nonpositive curvature

Tadeusz Januszkiewicz, Jacek Świątkowski (2006)

Publications Mathématiques de l'IHÉS

Similarity:

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...

Two signed associahedra.

Burgiel, H., Reiner, V. (1998)

The New York Journal of Mathematics [electronic only]

Similarity:

Combinatorial lemmas for polyhedrons

Adam Idzik, Konstanty Junosza-Szaniawski (2005)

Discussiones Mathematicae Graph Theory

Similarity:

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.

Brouwer Fixed Point Theorem for Simplexes

Karol Pąk (2011)

Formalized Mathematics

Similarity:

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....