Inverse Limit Spaces

Abstract

This paper is a vast survey of inverse limit spaces. After defining an inverse limit on continuous bonding functions, we prove important theorems about inverse limits, provide examples, and explore various generalizations of traditional inverse limits. In particular, we present original proofs of theorems given by Ingram and Mahavier in 'Inverse Limits of Upper Semi-Continuous Set Valued Functions.' We then use this new sort of inverse limit to enliven the notion of a 'two-sided' inverse limit; finally, we use inverse limits on u.s.c. functions to produce an indecomposable continuum.