Some properties of -dimensional generalized cubes
Władysław Kulpa (1995)
Acta Universitatis Carolinae. Mathematica et Physica
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Władysław Kulpa (1995)
Acta Universitatis Carolinae. Mathematica et Physica
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F. Javier Trigos-Arrieta, Marian Turzański (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Władysław Kulpa (1998)
Acta Universitatis Carolinae. Mathematica et Physica
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R. Molski (1965)
Fundamenta Mathematicae
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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.
Adam Idzik, Konstanty Junosza-Szaniawski (2006)
Discussiones Mathematicae Graph Theory
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We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also...
Buba-Brzozowa, Malgorzata (2000)
Journal for Geometry and Graphics
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J. M. Soriano (1990)
Collectanea Mathematica
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To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.
José María Soriano (1991)
Extracta Mathematicae
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