2000 | OriginalPaper | Buchkapitel
8. Some Extensions
verfasst von : Prof. Dr. Klaus Weihrauch
Erschienen in: Computable Analysis
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
In this book, we study computability concepts which are induced by notations and representations. Although every representation δ :⊆ Σω → M of a set induces a computability concept, only very few of them are useful. As an important class we have studied representations constructed from computable topological spaces (Sect. 3.2). Remember that every To-space with countable base can be extended to a computable topological space by an injective notation of a subbase. Many important To-spaces with countable base can be generated from separable metric spaces (Definition 2.2.1). Therefore, it is useful to study computability on metric spaces separately. The reader who is not familiar with the mathematical concepts used in this section is referred to any standard textbook on real analysis, for example, Rudin [Rud64].