The regular open‐open topology for function spaces

Source abstract

The regular open‐open topology, T r o o , is introduced, its properties for spaces of continuous functions are discussed, and T r o o is compared to T o o , the open‐open topology. It is then shown that T r o o on H ( X ), the collection of all self‐homeomorphisms on a topological space, ( X , T ), is equivalent to the topology induced on H ( X ) by a specific quasi‐uniformity on X , when X is a semi‐regular space.