Non--spaces
Šedivá-Trnková, Věra
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Šedivá-Trnková, Věra
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Erdös, P., Hajnal, A.
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de Vries, Jan
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Alas, O. T.
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Lev Birbrair, Alexandre C. G. Fernandes (2000)
Revista Matemática Complutense
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We present a complete bi-Lipschitz classification of germs of semialgebraic curves (semialgebraic sets of the dimension one). For this purpose we introduce the so-called Hölder Semicomplex, a bi-Lipschitz invariant. Hölder Semicomplex is the collection of all first exponents of Newton-Puiseux expansions, for all pairs of branches of a curve. We prove that two germs of curves are bi-Lipschitz equivalent if and only if the corresponding Hölder Semicomplexes are isomorphic. We also prove...