This is an announcement for the paper "The unit ball of the Hilbert space in its weak topology" by Antonio Aviles. Abstract: We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when the space is nonseparable. Archive classification: math.GN math.FA Mathematics Subject Classification: 46B50, 46B26, 46C05, 54B30, 54D15. Citation: Proc. Am. Math. Soc. 135, No. 3, 833-836 (2007) The source file(s), HilbertBall.tex: 14810 bytes, is(are) stored in gzipped form as 0903.0154.gz with size 5kb. The corresponding postcript file has gzipped size 57kb. Submitted from: avileslo@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0154 or http://arXiv.org/abs/0903.0154 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0154 or in gzipped form by using subject line get 0903.0154 to: math@arXiv.org.