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Category and Measure: Infinite Combinatorics, Topology and Groups (Cambridge Tracts in Mathematics, Series Number 233)
by: N. H. Bingham (Author), Adam J. Ostaszewski (Author)
Publisher: Cambridge University Press
Edition: 1st
Publication Date: 2025-01-23
Language: English
Print Length: 345 pages
ISBN-10: 0521196078
ISBN-13: 9780521196079
Book Description
Topological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a ‘continuity structure’, one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject’s current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.
Editorial Reviews
Topological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a ‘continuity structure’, one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject’s current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.
