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Publisher:
Cambridge University Press
Online publication date:
January 2025
Print publication year:
2025
Online ISBN:
9781139048057
DOI:
https://doi.org/10.1017/9781139048057
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
Series:
Cambridge Tracts in Mathematics (233)
Information

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.

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