A Sierpiński carpet with the co-Hopfian property
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- Merenkov, S. Invent. math. (2010) 180: 361. doi:10.1007/s00222-010-0231-5
Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian property for metric spaces and provide an example of a metric Sierpiński carpet with this property. As an application we obtain a quasi-isometrically co-Hopfian Gromov hyperbolic space with a Sierpiński carpet boundary at infinity. In addition, we give a complete description of the quasisymmetry group of the constructed Sierpiński carpet. This group is uncountable and coincides with the group of bi-Lipschitz transformations.