Monoidal Topology

A Categorical Approach to Order, Metric and Topology

Author: Dirk Hofmann,Gavin J. Seal,Walter Tholen

Publisher: Cambridge University Press

ISBN: 1107063949

Category: Mathematics

Page: 518

View: 5263

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Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.
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Programming Languages and Systems

28th European Symposium on Programming, ESOP 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, Prague, Czech Republic, April 6–11, 2019, Proceedings

Author: Luís Caires

Publisher: Springer

ISBN: 3030171841

Category: Computers

Page: 816

View: 5823

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This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019.
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Index Analysis

Approach Theory at Work

Author: R. Lowen

Publisher: Springer

ISBN: 1447164857

Category: Mathematics

Page: 466

View: 9590

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The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.
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