Mappings of the Sierpiński curve onto itself

Charatonik, J. J.

doi:10.1090/S0002-9939-1984-0749904-1

Mappings of the Sierpiński curve onto itself
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by J. J. Charatonik PDF

Proc. Amer. Math. Soc. 92 (1984), 125-132 Request permission

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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