A survey of the monolithic hyperspace problem
by
Henno Brandsma
University of Delft, Holland

A space X is called \aleph₀-monolithic if the closure of any countable subset of X has countable network weight. This notion originates in the theory of spaces of continuous functions, but is an interesting property in its own right. Arhangel'skij asked in 1987 when the hyperspace (the space of closed subsets of X endowed with the Vietoris topology) of a space is (\aleph₀-)monolithic. Since then several papers by Bell, and Brandsma and van Mill, have appeared on this problem. In this talk I will give a short survey of the results so far, most of which can be found in my thesis from september 1998. I hope to show that there are still some interesting questions in this area.

Date received: August 25, 1999

Copyright © 1999 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 # cadg-11.