Universal topological unary varieties. (Q1868867)

The author finds general conditions on a regular variety \(V\) of unary algebras such that the category \({\mathcal K}(V)\) is universal. The category \({\mathcal K}(V)\) consists of topological algebras, where the algebras belong to \(V\) and topologies belong to \(\mathcal K\). For \(\mathcal K\) one can take the category of connected paracompact spaces (with continuous maps or with continuous closed maps, or something in between).