Characterizing Inverse Sequences For Which Their Inverse Limits Are Homeomorphic

In [11], Mioduszewski characterized inverse sequences of polyhedrafor which their inverse limits are homeomorphic. In this article, we obtain amore general characterization: we characterize inverse sequences of arbitrary compactmetric spaces and continuous single-valued functions for which their inverselimits are homeomorphic. In our approach, set-valued functions are used insteadof continuous single-valued functions in almost commutative diagrams. Usingthis characterization we give an alternative proof that the Brouwer-Janiszewski-Knaster continuum and the pseudo-arc are circle-like continua.