On boundary arcs joining antipodal points of a planar convex body.
Averkov, Gennadiy (2006)
Beiträge zur Algebra und Geometrie
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Averkov, Gennadiy (2006)
Beiträge zur Algebra und Geometrie
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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 convex compact subset of εn with a non empty interior. This article is based on [15].
Karol Pąk (2014)
Formalized Mathematics
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In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic...
Bezdek, Károly, Connelly, Robert, Csikós, Balázs (2006)
Beiträge zur Algebra und Geometrie
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Hästö, Peter, Ibragimov, Zair (2007)
Annales Academiae Scientiarum Fennicae. Mathematica
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Zhang, Gaofei (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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Pier Luigi Papini (2004)
Extracta Mathematicae
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J. Katona, E. Molnár, I. Prok, J. Szirmai (2011)
Kragujevac Journal of Mathematics
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Karol Pąk (2014)
Formalized Mathematics
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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...
Samuel Amstutz, Imene Horchani, Mohamed Masmoudi (2005)
Control and Cybernetics
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Carter, Sheila, Craveiro de Carvalho, F.J. (2005)
Beiträge zur Algebra und Geometrie
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