CCC property of free topological groups
by
Kohzo Yamada
Auburn University and Shizuoka University
Coauthors: Gary Gruenhage (Auburn University)

Let F(X) and A(X) be respectively the free topological group and the free abelian topological group on a Tychonoff space X. For each n in \omega F_n(X) stands for a subset of F(X) formed by all words whose reduced length is less than equal to n. This concept is defined for A(X) in the same fashion. Since F(X) is the union of F_n(X), n in \omega and each F_n(X) is a continuous image of (X\oplusX^-1\oplus{e})ⁿ, if we assume MA, then it is easy to see that every F(X) on a ccc space X is also ccc. On the other hand, we show here that if we assume the existence of a Souslin line, then there is a ccc space X such that F(X) is not ccc. The same conditions are valid for A(X).

Date received: June 4, 1999