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.

The continuous structure of topological spaces is examined from the viewpoints of category and measure, with the former being paramount.

About the Author
N. H. Bingham is Emeritus Professor at Imperial College London. He is a probabilist with interests also in analysis, statistics, financial mathematics and history of mathematics, all of which he has taught extensively. He has written more than 160 papers and three books, and edited three others. Adam J. Ostaszewski is Professor at the London School of Economics. His research interests span set theory and topology (where he is known for Ostaszewski's clubs and Ostaszewski's space), and applications of real analysis to probability, economics and accounting. He is the author of more than 100 papers and three books.


Book Information
ISBN 9780521196079
Author N. H. Bingham
Format Hardback
Page Count 338
Imprint Cambridge University Press
Publisher Cambridge University Press