Markov-like generalized inverse systems and their limits (Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches)

Abstract

Markov interval maps were introduced by S. Holte [5] in 2002 and she showed that any two inverse limits with Markov interval bonding maps with the same pattern were homeomorphic. In 2013 I. Banič and T. Lunder [1] extended the notation from continuous maps to set-valued functions, called generalized Markov interval functions, and applied the theory of generalized inverse limits with set-valued functions. In this note we introduce Markov-like functions as a generalization of generalized Markov interval functions and show that any two generalized inverse limits with Markov-like bonding functions having same pattern are homeomorphic. Consequently we can give a generalization of [1].