The convergence and character spectra of compact spaces
by
Istvan Juhasz
Renyi Institute of Mathematics
Coauthors: W. Weiss

What can be said about the set of all lengths of convergent (transfinite) sequences in a compact space? Since in a compactum any point is the limit of a sequence whose length is equal to the character of the point, this question is closely related to the following: What can be said about the set of all characters of points taken in all (closed) subspaces of a given compactum? In particular, we shall examine and give partial results on the following question of Arhangelskii and Buzyakova: If the length of any convergent sequence in a compactum X has countable cofinality, is then X first countable?

Date received: June 23, 2008