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

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