CONTINUA THAT ADMIT EXPANSIVE Zn+1 ACTIONS BUT NOT EXPANSIVE Zn ACTIONS

A collection {h(1), ...h(n)} of commutative homeomorphisms on X generate an expansive Z(n) action on X provided that for some fixed c > 0 and every distinct x, y is an element of X there exist integers k1, ..., k(n) such that d(h(1)(k1) o h(2)(k2) o ...h(n)(kn) (x), h(1)(k1) o h(2)(k2) o ...h(n)(kn) (y)) >= c. For each set of positive integers k and n, a k-dimensional continuum X-k(n) is constructed such that X-k(n) admits an expansive Z(n+1) action but does not admit an expansive Z(n) action.