Recent research in affine differential geometry.
Soare, Nicolae (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Displaying similar documents to “Affine super-Pythagorean geometry.”
Recent research in affine differential geometry.
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On n-ary equivalence relations and their application to geometry
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CONTENTSForeword............................................................................................................................................. 5Introduction......................................................................................................................................... 7Chapter I. n-ary equivalence relations........................................................................................... 8Chapter II. Application of n-ary equivalence relations...
Affine bijections of C(X,I)
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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.