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arXiv · 1712.00526

Quasisymmetrically co-Hopfian Sierpi\'nski Spaces and Menger Curve

Hrant Hakobyan
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Abstract

A metric space $X$ is quasisymmetrically co-Hopfian if every quasisymmetric embedding of $X$ into itself is onto. We construct the first examples of metric spaces homeomorphic to the universal Menger curve and higher dimensional Sierpi\'nski spaces, which are quasisymmetrically co-Hopfian. We also show that the collection of quasisymmetric equivalence classes of spaces homeomorphic to the Menger curve is uncountable. These results answer a problem and generalize results of Merenkov from \cite{Mer:coHopf}.

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Hrant Hakobyan. 2017-12-02. Quasisymmetrically co-Hopfian Sierpi\'nski Spaces and Menger Curve. https://arxiv.org/abs/1712.00526

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