On affine geometric product objects
Józef Joachim Telega (1977)
Annales Polonici Mathematici
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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.
Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Takashi Kurose (1990)
Mathematische Zeitschrift
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Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Christoph Bandt, Mathias Mesing (2009)
Banach Center Publications
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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...
Michał Sadowski (1990)
Colloquium Mathematicae
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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.
Udo Simon, An-Mi Li, Luc Vrancken (1991)
Mathematische Zeitschrift
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Bach, Andrea K. (1997)
Beiträge zur Algebra und Geometrie
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Papi, Paolo (1997)
The Electronic Journal of Combinatorics [electronic only]
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Joachim Schmid (1995)
Manuscripta mathematica
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John Smillie (1981)
Inventiones mathematicae
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Michel Talagrand (1984)
Mathematica Scandinavica
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R.V. Gurjahr (1980)
Inventiones mathematicae
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