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Homotopy and the Kestelman-Borwein-Ditor theorem

Bingham, N. H. and Ostaszewski, A. J. (2011) Homotopy and the Kestelman-Borwein-Ditor theorem. Canadian Mathematical Bulletin, 54 (1). pp. 12-20. ISSN 0008-4395

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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.

Item Type: Article
Official URL:
Additional Information: © 2011 Canadian Mathematical Society
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 01 Dec 2010 12:37

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