| 期刊全称 | Apartness and Uniformity | | 期刊简称 | A Constructive Devel | | 影响因子2023 | Douglas S. Bridges,Luminiţa Simona Vîţă | | 视频video | | | 发行地址 | This is the first research monograph on this topic.Suitable for advanced researchers in computer science, mathematics and logic.The authors are established experts on this subject.Includes supplementa | | 学科分类 | Theory and Applications of Computability | | 图书封面 |  | | 影响因子 | .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 author | | Pindex | Book 2011 |
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发表于 2025-3-21 17:01:33
