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Mappings of the Sierpiński curve onto itself

Author: J. J. Charatonik
Journal: Proc. Amer. Math. Soc. 92 (1984), 125-132
MSC: Primary 54F15; Secondary 54F50
MathSciNet review: 749904
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Abstract: Given two points $ p$ and $ q$ of the Sierpiński universal plane curve $ S$, necessary and/or sufficient conditions are discussed in the paper under which there is a mapping $ f$ of $ S$ onto itself such that $ f(p) = q$ and $ f$ belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.

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Keywords: Universal plane curve, rational part, local homeomorphism, open, simple, monotone mappings
Article copyright: © Copyright 1984 American Mathematical Society