Uniformizing (proximal) \(\varDelta\)-topologies. (Q1426508)

The authors investigate necessary and sufficient conditions for the uniformizability of (proximal) \(\Delta\)-topologies. They attack this problem using a tool from uniform topology, namely the Attouch-Wets uniformities. Similar investigations in the past have used the construction of special Urysohn functions instead. Their study also deals with uniformizability of so-called \(\Delta U\)-topologies and proximal \(\Delta U\)-topologies, which are defined as natural generalizations of the \(U\)-topology introduced by Costantini and Vitolo. Furthermore, conditions are determined under which these latter topologies are second countable, first countable or metrizable.