Transfinite Induction with Control
by
Alan Dow
York University

Transfinite induction is certainly a common method in topology and, given the large number of topological examples constructed in this way, it could well be considered a "topological method". Many constructions are motivated by questions in related fields. We suppress mention of special set-theoretic axioms until the talk.

In response to questions of Hansell, we have, with Junilla and Pelant, examples of compact scattered spaces K with the property that C_p(K) fails to be \sigma-relatively compact.

Gary Faulkner asked for a sequentially compact space X which has a compactification which is not sequentially compact. There's an easy example in ZFC and we discuss the possibility of there being a separable example.

We also consider the question of the existence of a compact space X which does not contain the smallest infinite compact separable space (the converging sequence) nor the largest (\betaN).

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-08.