A Sierpiński carpet with the co-Hopfian property (Q967586)

Motivated by questions in geometric group theory, the author defines a quasisymmetric co-Hopfian property for metric spaces and provides an example of a metric Sierpiński carpet with this property. As an application the author obtains a quasi-isometrically co-Hopfian Gromov hyperbolic space with a Sierpiński carpet boundary at infinity. In addition, the author gives 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.