We investigate a quasisymmetrically invariant counterpart of the topological
Hausdorff dimension of a metric space. This invariant, called the topological
conformal dimension, gives a lower bound on the topological Hausdorff dimension
of quasisymmetric images of the space. We obtain results concerning the
behavior of this quantity under products and unions, and compute it for some
classical fractals. The range of possible values of the topological conformal
dimension is also considered, and we show that this quantity can be fractional.Comment: 16 pages, revised after referee's reports. To appear in Conformal
Geometry and Dynamic
