Open Universals
by
Paul Gartside
Merton College, Oxford
Coauthors: Jo Lo (St Edmund Hall, Oxford)

Let X and Y be spaces. An open subset U of X ×Y is an open universal for X parametrised by Y if every open subset of X is a horizontal slice through U. Informally then, the space Y `codes' the topology of X.

Every space has an open universal coded by a compact space, and another open universal parametrised by a discrete space; but which spaces have universals parametrised by a ``small and nice'' space?

In this talk we investigate those spaces with open universals coded by second countable, hereditarily separable or hereditarily Lindelof spaces.

Date received: August 18, 1999