On collectionwise normal metalindelof spaces
by
Zoltan Balogh
Miami University

In 1972, R. Hodel (and later S. Watson and D. Burke) asked the question whether every collectionwise normal, metalindelof space is paracompact.

The following theorem answers this in the negative. Theorem. There is a hereditarily metalindelof, hereditarily collectionwise normal, realcompact Dowker space. The space above also answers in ZFC a question of M.E. Rudin from 1971: Is there a realcompact Dowker space?

We will then discuss work in progress concerning the following question of D. Burke:

Is every metalindelof, collectionwise normal and countably paracompact space paracompact?

Date received: March 5, 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 # caca-59.