Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2007-27

November 2007


Homotopy and the Kestelman-Borwein-Ditor Theorem

N. H. Bingham and A. J. Ostaszewski

The Kestelman-Borwein-Ditor Theorem, on embedding a null sequence by translation in (measure/category) `large' sets, has two generalizations. Miller MilH replaces the translated sequence by a `sequence homotopic to the identity'. The authors, in Research Report LSE-CDAM-2007-26, replace points by functions: a uniform functional null sequence replaces the null sequence and translation receives a functional form. We give a unified approach to results of this kind. In particular, we show that (i) Miller's homotopy version follows from the functional version, and (ii) the pointwise instance of the functional version follows from Miller's homotopy version.

A PDF file (110 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2007-27, together with your name and postal address to:
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 


Introduction to the CDAM Research Report Series.
CDAM Homepage.


Copyright © London School of Economics & Political Science 2007