Some remarks about compact separable spaces
by
Alan Dow
York University

There are many interesting questions and results about the relationships between various kinds of convergence conditions in small compact (separable) spaces. For example, what is the effect of demanding that every countable sequence has a converging subsequence? Or that there is a sequence which has no converging subsequence? A better known (solved problem) asks if countable tightness (closure determined by countable sets) implies sequential (closure determined by converging sequences).

We will discuss at least one such question. Efimov's question is the following: "Does every compact space contain a copy of either \omega+ 1 (the converging sequence) or \beta\omega ?". This is a most extreme kind of dichotomy possible. We will discuss the influence of the Proper Forcing Axiom on Efimov's question.

Date received: March 18, 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 # caac-12.