SELF-SIMILARITY IN INVERSE LIMIT SPACES OF THE TENT FAMILY

Taking inverse limits of the one-parameter family of tent maps of the interval generates a one-parameter family of inverse limit spaces. We prove that, for a dense set of parameters, these spaces are locally, a t most points, the product of a Canter set and an are. On the other ha nd, we show that there is a dense G(delta) set of parameters for which the corresponding space has the property that each neighborhood in th e space contains homeomorphic copies of every inverse limit of a tent map.