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Titlebook: Relational Topology; Gunther Schmidt,Michael Winter Book 2018 Springer International Publishing AG, part of Springer Nature 2018 Relationa

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發(fā)表于 2025-3-21 17:49:22 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Relational Topology
編輯Gunther Schmidt,Michael Winter
視頻videohttp://file.papertrans.cn/827/826113/826113.mp4
概述Introduces and develops an algebraic treatment of Boolean matrices.Applies the methods to give an algebraic treatment of point set topology.Offers a framework for handling topological problems using t
叢書(shū)名稱Lecture Notes in Mathematics
圖書(shū)封面Titlebook: Relational Topology;  Gunther Schmidt,Michael Winter Book 2018 Springer International Publishing AG, part of Springer Nature 2018 Relationa
描述.This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science.. .Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants..
出版日期Book 2018
關(guān)鍵詞Relational Mathematics; Algebraic Topology; Spatial Reasoning; Kronecker Product of Relations; Frames in
版次1
doihttps://doi.org/10.1007/978-3-319-74451-3
isbn_softcover978-3-319-74450-6
isbn_ebook978-3-319-74451-3Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer International Publishing AG, part of Springer Nature 2018
The information of publication is updating

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沙發(fā)
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Prerequisites,cular from Schmidt and Str?hlein (Relationen und Graphen. Mathematik für Informatiker. Springer, 1989; Relations and graphs—discrete mathematics for computer scientists. EATCS monographs on theoretical computer science. Springer, 1993), Schmidt (Relational mathematics. Encyclopedia of mathematics an
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發(fā)表于 2025-3-22 09:45:27 | 只看該作者
Meet and Join as Relations,. This concerned the very general concepts such as being commutative, distributive, or associative. A more specific law concerns absorption mainly occurring in one traditional environment, namely for binary meets and joins. They will be handled here accordingly when the following cone mappings are a
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Proximity and Nearness,are point-to-set notions that characterize being element of a neighborhood or of an open set. The first concept of proximity was described in 1908 by Frigyes Riesz and then ignored. Others to be mentioned for having worked on such ideas include V. A. Efremovi? in 1934 and A. N. Wallace in 1940. More
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Frames,bserve without any knowledge about its inner program or process structure. This means necessarily incomplete observations which are somehow ordered by precision. Handling such observations requires specific orderings and often entails employing topological concepts.
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Book 2018braically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants..
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發(fā)表于 2025-3-23 08:49:43 | 只看該作者
Applying Relations in Topology,oint-free as well as quantifier-free versions, showing how they are interrelated, thus exhibiting their cryptomorphism and offering the possibility to transform one version into the other, not least visualizing them via . programs.
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