Classification of -cubes in the dimension
Jozef Tvarožek (1986)
Mathematica Slovaca
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Jozef Tvarožek (1986)
Mathematica Slovaca
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Jozef Tvarožek (1986)
Mathematica Slovaca
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J. Cannon, R. Daverman (1981)
Fundamenta Mathematicae
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Marian Trenkler (2001)
Acta Arithmetica
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O. Ramaré (2005)
Acta Arithmetica
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Krzysztof Jan Nowak (2009)
Annales Polonici Mathematici
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The main purpose of this paper is to present a natural method of decomposition into special cubes and to demonstrate how it makes it possible to efficiently achieve many well-known fundamental results from quasianalytic geometry as, for instance, Gabrielov's complement theorem, o-minimality or quasianalytic cell decomposition.
Robert Daverman, William Eaton (1969)
Fundamenta Mathematicae
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Stephen Semmes (2000)
Revista Matemática Iberoamericana
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In [6], Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images (in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz, with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and uniform rectifiability of sets, as in [6], [7], [11], [13]. Some special cases of David's results, concerning...