Abstract:
Inverse limits are topological spaces that are determined by an inverse sequence of continuous functions (called bonding maps). They have been extensively studied and a great deal is known about them. One central fact about inverse limits is the so-called Subsequence Theorem, which ensures that the homeomorphism type of an inverse limit is not affected when we “collapse” portions of the inverse sequence by function composition. More recently, the notion of generalised inverse limits was introduced in [1]. These involve bonding maps that are upper semi-continuous set-valued functions. In this context, we do not have a direct generalisation of the Subsequence Theorem. The question of which sets of conditions on a generalised inverse sequence ensure that an analogue of the Subsequence Theorem holds in the generalised context was raised in [2]. The purpose of this thesis is to provide one possible answer.