This is an announcement for the paper "Countable products of spaces of finite sets" by Antonio Aviles. Abstract: We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification. Archive classification: math.GN math.FA Mathematics Subject Classification: 46B50, 46B26, 54B10, 54D30 Citation: Fundamenta Math. 186, No. 2, 147-159 (2005) The source file(s), SigmakProducts.tex: 40152 bytes, is(are) stored in gzipped form as 0903.0068.gz with size 12kb. The corresponding postcript file has gzipped size 102kb. Submitted from: avileslo@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0068 or http://arXiv.org/abs/0903.0068 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0068 or in gzipped form by using subject line get 0903.0068 to: math@arXiv.org.