An analogue of the Krein-Milman theorem for star-shaped sets.
Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Kharazishvili, A. (2003)
Georgian Mathematical Journal
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Caruso, A. (2002)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Karol Pąk (2010)
Formalized Mathematics
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In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...
Gennadiy Averkov (2003)
Extracta Mathematicae
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Jaume, Daniel A., Puente, Rubén (2005)
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].
Soltan, Valeriu (2006)
Beiträge zur Algebra und Geometrie
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Martini, Horst, Wenzel, Walter (2004)
Beiträge zur Algebra und Geometrie
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E. Ignaczak, A. Paszkiewicz (1998)
Applicationes Mathematicae
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We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
Sehie Park, Jong Park (1996)
Colloquium Mathematicae
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