Brown’s Approximation Theorem

Abstract

This chapter is devoted to an approximation theorem that allows certain adjustments of the bonding mappings in an inverse limit sequence without altering the topology of the inverse limit. We apply this fundamental result to show that if f is a mapping of an interval J onto itself that is the union of two monotone maps from nonoverlapping subintervals onto J, then the inverse limit using f as a single bonding map is the familiar BJK horseshoe.