Abelian groups admitting a Frechet-Urysohn pseudocompact topological group topology

作者：Tkachenko Mikhail^*

来源：Journal of Pure and Applied Algebra, 2010, 214(7): 1103-1109.

DOI：10.1016/j.jpaa.2009.09.016

We show that every Abelian group G with r(0)(G) = vertical bar G vertical bar = vertical bar G vertical bar(omega) admits a pseudocompact Hausdorff topological group topology T such that the space (G, T) is Frechet-Urysohn. We also show that a bounded torsion Abelian group G of exponent n admits a pseudocompact Hausdorff topological group topology making G a Frechet-Urysohn space if for every prime divisor p of n and every integer k >= 0, the Ulm-Kaplansky invariant f(p,k) of G satisfies (f(p,k))(omega) = f(p,k) provided that f(p,k) is infinite and f(p,k) > f(p,i) for each i > k.
Our approach is based on an appropriate dense embedding of a group G into a Sigma-product of circle groups or finite cyclic groups.

• 出版日期2010-7