More on Continuously Urysohn Spaces
by
David Lutzer
College of William and Mary
Coauthors: H. Bennett (Texas Tech University)

A space X is continuously Urysohn if there is a continuous function \Psi: X² - \Delta --> C(X), where C(X) carries the topoogy of uniform convergence, such that if we write f_{x, y} = \Psi(x, y), then f_{x, y}(x) =/= f_{x, y}(y). In this paper we use ordered space constructions to investigate the role of strong base properties (such as the existence of a point-countable base, or of a \sigma-disjoint base) in continuously Urysohn spaces.

Date received: July 6, 2000