  We prove that every free group G with infinitely many generators admits a
Hausdorff group topology T with the following property: for every T-open
neighbourhood U of the identity of G, each element g in G can be represented as
a product g=g_1 g_2 ... g_k such that the cyclic group generated by each g_i is
contained in U. In particular, G admits a Hausdorff group topology with the
small subgroup generating property of Gould. This provides a positive answer to
a question of Comfort and Gould in the case of free groups with infinitely many
generators. The case of free groups with finitely many generators remains open.

General Topology;Functional Analysis;Group Theory