Topological properties of concept spaces (full version)

Based on the observation that the category of concept spaces with the positive information topology is equivalent to the category of countably based T0 topological spaces, we investigate further connections between the learning in the limit model of inductive inference and topology. In particular, we show that the “texts” or “positive presentations” of concepts in inductive inference can be viewed as special cases of the “admissible representations” of computable analysis. We also show that several structural properties of concept spaces have well known topological equivalents. In addition to topological methods, we use algebraic closure operators to analyze the structure of concept spaces, and we show the connection between these two approaches. The goal of this paper is not only to introduce new perspectives to learning theorists, but also to present the field of inductive inference in a way more accessible to domain theorists and topologists.