Monolithicity of Hyperspaces
by
Henno Brandsma
Vrije Universeit AMsterdam
Coauthors: Jan van Mill

A space X is called monolithic if network weight equals density for all closed subsets of X. Arhangel'skii asked the question when the Vietoris hyperspace H(X) of X is monolithic. Recently, Bell has found that necessary conditions on X are: X is monolithic, compact and hereditary Lindelöf. He could prove these conditions to be sufficient for the class of ordered topological spaces.

This talk will deal with two new results around this question: We extend Bell's result for ordered spaces to a class containing the monotonically normal spaces. Moreover, we will prove that spaces that are constructed like Kunen's famous L-space, do not have a monolithic hyperspace, improving a result earlier obtained by the present authors.

Date received: June 30, 1997

Copyright © 1997 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 # caao-42.