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Homotopy and the Kestelman-Borwein-Ditor theorem

By 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 replaces the translated sequence by a "sequence homotopic to the identity". The authors, in a previous paper, 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

Topics: QA Mathematics
Publisher: Canadian Mathematical Society
Year: 2011
DOI identifier: 10.4153/CMB-2010-093-4
OAI identifier:
Provided by: LSE Research Online
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