Bis zu 50 % günstiger als neu 3 Jahre rebuy Garantie Professionelles Refurbishment

Handgeprüfte Gebrauchtware

Bis zu 50 % günstiger als neu

Der Umwelt zuliebe

Apartness and Uniformity

Douglas S. Bridges, Luminiţa Simona Vîţă (Broschiert, Englisch)

Keine Bewertungen vorhanden

Weitere Ausgaben

Optischer Zustand

Beschreibung

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-based theory of proximity spaces provides some guidance for the theory of apartness, the notion of nearness/proximity does not embody enough algorithmic information for a deep constructive development. The use of constructive (intuitionistic) logic in this book requires much more technical ingenuity than one finds in classical proximity theory -- algorithmic information does not come cheaply -- but it often reveals distinctions that are rendered invisible by classical logic. In the first chapter the authors outline informal constructive logic and set theory, and, briefly, the basic notions and notations for metric and topological spaces. In the second they introduce axioms for a point-set apartness and then explore some of the consequences of those axioms. In particular, they examine a natural topology associated with an apartness space, and relations between various types of continuity of mappings. In the third chapter the authors extend the notion of point-set (pre-)apartness axiomatically to one of (pre-)apartness between subsets of an inhabited set. They then provide axioms for a quasiuniform space, perhaps the most important type of set-set apartness space. Quasiuniform spaces play a major role in the remainder of the chapter, which covers such topics as the connection between uniform and strong continuity (arguably the most technically difficult part of the book), apartness and convergence in function spaces, types of completeness, and neat compactness. Each chapter has a Notes section, in which are found comments on the definitions, results, and proofs, as well as occasional pointers to future work. The book ends with a Postlude that refers to other constructive approaches to topology, with emphasis on the relation between apartness spaces and formal topology. Largely an exposition of the authors' own research, this is the first book dealing with the apartness approach to constructive topology, and is a valuable addition to the literature on constructive mathematics and on topology in computer science. It is aimed at graduate students and advanced researchers in theoretical computer science, mathematics, and logic who are interested in constructive/algorithmic aspects of topology. Weniger zeigen

106,99 €

Broschiert | Neu

oder

Auf Lager

Versandbereit in 2-3 Werktagen

zzgl.

Du kannst wie immer einen Kaufalarm setzen, wenn du auf das gebrauchte Buch warten möchtest.

Auf Lager

Versandbereit in 2-3 Werktagen

zzgl.

Handgeprüfte Gebrauchtware

Bis zu 50 % günstiger als neu

Der Umwelt zuliebe

Produktinformationen

Technische Daten

Erscheinungsdatum

27.11.2013

Sprache

Englisch

EAN

9783642269967

Herausgeber

Springer Berlin

Serien- oder Bandtitel

Theory and Applications of Computability

Sonderedition

Nein

Autor

Douglas S. Bridges, Luminiţa Simona Vîţă

Seitenanzahl

198

Einbandart

Broschiert

Buch Untertitel

A Constructive Development

Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com

Warnhinweise und Sicherheitsinformationen

Informationen nach EU Data Act

Bewertungen

-.-

Leider noch keine Bewertungen

Sicher bei rebuy kaufen

Sehr Gut, 4.52/5.00

Aus 200.000+ Bewertungen

Schreib die erste Bewertung für dieses Produkt!

Wenn du eine Bewertung für dieses Produkt schreibst, hilfst du allen Kund:innen, die noch überlegen, ob sie das Produkt kaufen wollen. Vielen Dank, dass du mitmachst!