Supersequential spaces
by
Alan Dow
University of North Carolina at Charlotte

Motivated by the Moore-Mrowka problem which asks if compact spaces of countable tightness are sequential, we investigate the extent to which compact sequential spaces might be Frechet. A space is Frechet if the closure of a set is simply all limits of converging subsequences. A space is sequential if iterating this attaching of limits of converging sequences arrives at the closure. The sequential order of a space is the ordinal number of times that the adding of limits of converging sequences must be iterated in order to arrive at the closure. We are interested in the question of how large this sequential order can be.

Date received: February 27, 2008