Abstract
It is a well-known fact that there are continua X such that the inverse limit of any inverse sequence {X,f_n} with surjective continuous bonding functions f_n is homeomorphic to X. The pseudoarc or any Cook continuum are examples of such continua. Recently, a large family of continua X was constructed in such a way that X is frac{1}{m}-rigid and the inverse limit of any inverse sequence {X,f_n} with surjective continuous bonding functions f_n is homeomorphic to X by Banič and Kac. In this paper, we construct an uncountable family of pairwise non-homeomorphic continua X such that X is 0-rigid and prove that for any sequence (f_n) of continuous surjections on X, the inverse limit varprojlim {X,f_n} is homeomorphic to X.
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