Open Universal Sets
by
P. J. Collins
Oxford University, United Kingdom

An open subset U of X ×Y is an open universal set for X parametrised by Y if, for every open V in X, there is an element y of Y such that V = { x : (x, y) in U }. The existence of open universal sets gives unusual results on hereditary density and hereditary cellularity, connecting a space X and a space Y parametrising it, which can be strengthened in face of compactness or a G_\delta diagonal. That 'every compact zero-dimensional space with an open universal set parametrised by a space with the hereditary c.c.c. is metrisable' is consistent and independent of ZFC. Authors involved include P.M. Gartside, R.W. Knight and J.T.H. Lo.

Date received: June 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeh-34.