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Apartness and Uniformity: A Constructive Development (Theory and Applications of Computability) by Bridges, D. S. (Douglas S.), 1945- author, Vîță, Luminița Simona, author is a nonfiction available to read on EtoBox.

What is Apartness and Uniformity: A Constructive Development (Theory and Applications of Computability) about?

XIV, 198 p 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

Who reads Apartness and Uniformity: A Constructive Development (Theory and Applications of Computability)?

Author

Bridges, D. S. (Douglas S.), 1945- author, Vîță, Luminița Simona, author

Publisher

Berlin, Heidelberg : Springer Berlin Heidelberg

Published

2011

Language

EN

ISBN

9783642224140

Category

nonfiction

Subjects

Mathematics, Computer Science, Stem