Characterizing Inverse Sequences For Which Their Inverse Limits Are Homeomorphic

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