Controlled Hahn-Mazurkiewicz Theorem and some new dimension functions of Peano continua |
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Authors: | T. Banakh M. Tuncali |
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Affiliation: | a Nipissing University, North Bay, Canada b Akademia ?wi?tokrzyska, Kielce, Poland c Lviv National University, Lviv, Ukraine |
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Abstract: | Given a metric Peano continuum X we introduce and study the Hölder Dimension there is a -Hölder onto map of X as well as its topological counterpart is an admissible metric for X}. We show that for each convex metric continuum X the dimension Hö-dim(X) equals the fractal dimension of X. The topological Hölder dimension Hö-dim(Mn) of the n-dimensional universal Menger cube Mn equals n. On the other hand, there are 1-dimensional rim-finite Peano continua X with arbitrary prescribed Hö-dim(X)?1. |
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Keywords: | Peano continuum Fractal dimension Hö lder map |
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