The regular open-open topology for function spaces (Q1912324)

Summary: The regular open-open topology, \(T_{\text{roo}}\), is introduced, its properties for spaces of continuous functions are discussed, and \(T_{\text{roo}}\) is compared to \(T_{\text{oo}}\), the open-open topology. It is then shown that \(T_{\text{roo}}\) 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.