Resumen de Inverse limits with set valued functions

Van Nall

• We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [0,1] to the set of closed subsets of [0,1]. Several continua including [0,1]×[0,1] and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional pointvalues, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.