TIGHTNESS OF FREE ABELIAN TOPOLOGICAL GROUPS AND OF FINITE PRODUCTS OF SEQUENTIAL FANS

Let A(X) be the free abelian topological group on a Tychonoff space X , and S (/'l:) the sequential fan with /'l:-many spines, which is the quotient space obtained from C(/'l:) which is the disjoint union of /'l:-many con­ vergent sequences by identifying all the limit points to a single point. Then we proved that the tightness of A 2n (C(K)) is equal to that of S(K)n for each n E N. As a corollary, we get if /'l: is an infinite cardinal with K = W or cf(/'l:) > w, n E N and X is a metrizable space