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
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.
|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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