Group action on \(\mathbb R\times \mathbb Q\) and fine group topologies
Under a number of conditions on the base space \(X\), for example T\(_2\) rim-compact and locally connected, the lattice of admissible group topologies on the space \(\mathcal H(X)\) of homeomorphisms, i.e. those topologies for which the evaluation \(\mathcal H(X)\times X\to X\) is continuous, has a least element. A converse, whether non-rim-compact spaces may have this property, is answered by identifying a least element of the lattice of admissible topology on the non-rim-compact space \(\mathbb R\times\mathbb Q\).
fine uniform topology w.r.t. a class of metrics
fine group topology with respect to a class of metrics
scientific article; zbMATH DE number 5539520
scientific article