Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1890)
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Table of contents (9 chapters)
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Front Matter
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Distributions and Complete Spreads
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Front Matter
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An Axiomatic Theory of Complete Spreads
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Front Matter
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Aspects of Distributions and Complete Spreads
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Front Matter
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Back Matter
Keywords
About this book
The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads in topology due to R. H. Fox (1957) but, unlike the classical theory, it emphasizes an unexpected connection with topos distributions in the sense of F. W. Lawvere (1983). The constructions, though often motivated by classical theories, are sometimes quite different from them. Special classes of distributions and of complete spreads, inspired respectively by functional analysis and topology, are studied. Among the former are the probability distributions; the branched coverings are singled out amongst the latter.
This volume may also be used as a textbook for an advanced one-year graduate course introducing topos theory with an emphasis on geometric applications. Throughout the authors emphasize open problems. Several routine proofs are left as exercises, but also as ‘exercises’ the reader will find open questions for possible future work in a variety of topics in mathematics that can profit from a categorical approach.
Authors and Affiliations
About the authors
Marta Bunge was born in Argentina where she studied philosophy and mathematics. She did her graduate work in mathematics at the University of Pennsylvania where she obtained her Ph. D. degree in 1966 under the supervision of Peter Freyd and F. William Lawvere. She has worked at McGill University since 1966, where she is currently Professor Emerita. She has been a visitor at mathematics institutes in Aarhus, Zurich, Mexico, Geneva, Mallorca, Genoa, and Sydney.
Jonathon Funk was born in Saskatchewan where he studied mathematics before coming to McGill University, where in 1991 he completed a Ph. D. under the supervision of Marta Bunge. Since then he has worked in Newfoundland, Cyprus, British Columbia, and Regina. Presently, he is Lecturer at the University of the West Indies in Barbados. He has been a visitor to McGill University on several occasions.
Bibliographic Information
Book Title: Singular Coverings of Toposes
Authors: Marta Bunge, Jonathon Funk
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/3-540-36359-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-36359-0Published: 21 August 2006
eBook ISBN: 978-3-540-36360-6Published: 19 January 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 225
Number of Illustrations: 3 b/w illustrations
Topics: Category Theory, Homological Algebra, Manifolds and Cell Complexes (incl. Diff.Topology), Order, Lattices, Ordered Algebraic Structures