A Natural Weak Limit Space with Admissible Representation which is not a Limit Space
Matthias Schröder · Electronic Notes in Theoretical Computer Science · 2002
Weak limit spaces are a generalization of limit spaces and thus of topological spaces. They describe the approximation structure induced by a representation more appropriately than topological spaces or limit spaces. Representations are used in Type Two Theory of Effectivity (TTE) to define computability on uncountable sets. We give an example for a natural weak limit space which fails to be a limit space. Its underlying set are the regularly closed sets of real numbers and its convergence relation is the one induced by an admissible, naturally defined representation of the regularly closed sets.