Topological Characteristics of Harmonic Quasiconformal Unit Disk Automorphisms in the Uniform Topology

Abstract: We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this space of mappings are investigated, such as separability, compactness, path--connectedness and completeness.