Resumen de Mapping Theorems for Rigid Continua and Their Inverse Limits

Iztok Banic, Teja Kac

• We give mapping theorems for certain families of rigid continua; i.e., we prove a mapping theorem for stars, paths and cycles of Cook continua. We also introduce the degree of rigidity of a continuum, the notion of 1 n -rigid continua and prove some existence theorems for 1 n -rigid continua. We also construct a non-trivial infinite family of pairwise non-homeomorphic continua X with the property that for any sequence ( fn) of continuous surjections fn : X → X, the inverse limit lim←−{X, fi}∞ i=1 is homeomorphic to X. Explicitly, we show that for each positive integer n, every 1 n -rigid continuum has this property.