The Problem of Consonance and Complete Metrizability
by
Stephen Watson
York University

A space is said to be consonant if the upper Kuratowski convergence on the hyperspace of closed sets coincides with its cocompact topology. It is surprisingly non-trivial to establish even that the rational numbers fail to be consonant (this was done independently by Bouziad, first, and then, Saint-Raymond, Fremlin, and Costantini and the author) and that completely metrizable spaces are indeed consonant (this was established by Dolecki, Greco and Lechicki). It seems to be a difficult problem to decide whether consonance coincides (in separable metrizable spaces) with complete metrizability. We give some partial results on this problem which were obtained jointly with Camillo Costantini of Universita di Torino in Italy.

Date received: February 29, 1996

Copyright © 1996 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 # caad-10.