Uniformly open mappings and uniform embeddings of function spaces (Q1343823)

The authors begin the study of uniformly open mappings which appear in many diverse situations. They show that all continuous open surjections between compact Hausdorff spaces are uniformly open and relate perfect maps to uniformly open maps on hyperspaces. Next they consider inverse systems of uniform spaces. The second part of the paper deals with uniform embeddings into hyperspaces and these involve uniformly open maps. This reviewer's idea of embedding g a function space into a hyperspace [Quest. Answers Gen. Topology 9, No. 1, 33-60 (1991; Zbl 0717.54005)]\ is used to study completion of function spaces with respect to the Hausdorff uniformity. Some related unsolved problems are mentioned.