Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2007-29

November 2007 (Revised January 2009)

Bitopology and measure-category duality

N. H. Bingham and A. J. Ostaszewski

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density toplologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. As a by-product we give a unified proof of the measure and category cases of Uniform Convergence Theorem for slowly varying functions.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk