This is an announcement for the paper "Locally uniformly convex norms in Banach spaces and their duals" by Richard Haydon. Abstract: It is shown that a Banach space with locally uniformly convex norm admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: 46B20 The source file(s), LURnormsAndDuals.tex: 50635 bytes, is(are) stored in gzipped form as 0610420.gz with size 15kb. The corresponding postcript file has gzipped size 65kb. Submitted from: richard.haydon@bnc.ox.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0610420 or http://arXiv.org/abs/math.FA/0610420 or by email in unzipped form by transmitting an empty message with subject line uget 0610420 or in gzipped form by using subject line get 0610420 to: math@arXiv.org.