Summer Conference on Topology and Its Applications


QH-Singularity of Quasi-Uniform Spaces


Tom Vroegrijk

Document Type

Topology + Asymmetric Structures

Publication Date


Publication Source

32nd Summer Conference on Topology and Its Applications


In the book Uniform Spaces by Isbell it is wrongfully claimed that the Hausdorff uniformities associated with two distinct uniform structures on a set X define distinct hyperspace topologies. The question for which uniformities this claim is in fact true became known as the Isbell-Smith problem. In this talk we will take a closer look at the Isbell-Smith problem for quasi-uniform spaces. In particular, we will study the properties of QH-singular quasi-uniform spaces and describe the QH-equivalence class of a transitive quasi-uniformity.