The character of free and free abelian topological groups
by
Peter Nickolas
University of Wollongong
Coauthors: Mikhail Tkachenko (Universidad Autónoma Metropolitana, Mexico)

The character of a topological group is the smallest (infinite) cardinal of a local base at the identity. Denote by F(X) and A(X) the free and free abelian topological groups, respectively, on a Tychonoff space X. This talk surveys work of the speaker and the coauthor on the characters \chi(F(X)) and \chi(A(X)) of these groups, concentrating on the cases where X is compact and where X is metrizable. It is shown that when X is compact, \chi(F(X)) and \chi(A(X)) are equal and that their value, which is computed explicitly, depends only on the weight of X. In particular, when X is compact and metrizable this value is the well known ``small cardinal'' \mathfrakd, the least cardinal of a dominating set in ^\omega\omega. When X is non-compact and metrizable, it is shown that the values of \chi(F(X)) and \chi(A(X)) can differ arbitrarily largely.

Date received: May 14, 2001

Copyright © 2001 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 # cagw-33.