| Description |
In the first chapter, minimal sequences and minimality detectors are defined in the context of compact metric spaces. Sequence A001511 is used to show that minimality detection with respect to N is equivalent to minimality detection with respect to Z. It is shown that a compact space Y is a minimality detector for a compact space X if and only if every finite set of points in X is isolated by some continuous map from X to Y . Necessary conditions are given for one finite graph to be a minimality detector for another and it is shown that two finite graphs cannot be mutual minimality detectors unless they are homeomorphic. In the second chapter, we build upon the work of Climenhaga and Thompson to show that a dense set of parameters B,a with B > 2 give rise to Ba shift spaces for which all Holder continuous functions have unique equilibrium states. |
