Characterizing inverse sequences for which their inverse limits are homeomorphicČrepnjak, Matevž (Avtor) Sovič, Tina (Avtor) inverse limitcompact metric spaceset-valued functionIn [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.Springer Nature (Akadémiai Kiadó)20242025-02-27 15:35:31Znanstveno delo91913sl© 2024 The Author(s)