An Obstruction to the Existence of Affine Structures.
John Smillie (1981)
Inventiones mathematicae
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John Smillie (1981)
Inventiones mathematicae
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Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Janko Marovt (2006)
Studia Mathematica
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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.
Michał Sadowski (1990)
Colloquium Mathematicae
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Paweł Urbański (2003)
Banach Center Publications
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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
Takashi Kurose (1990)
Mathematische Zeitschrift
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Ivan Kolář, Marco Modugno (1990)
Czechoslovak Mathematical Journal
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A. Moór, Dj.F. Nadj (1980)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Takashi Sano (1999)
Banach Center Publications
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We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.
Paweł Witowicz (1995)
Annales Polonici Mathematici
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For a submanifold of of any codimension the notion of type number is introduced. Under the assumption that the type number is greater than 1 an equivalence theorem is proved.