This is an announcement for the paper "Convexity of Chebyshev sets through differentiability of distance function" by Assadi, Hadi Haghshenas, and Hosseini Guive. Abstract: The aim of this paper is to present some equivalent conditions that ensure the convexity of a Chebyshev set. To do so, we use Gateaux differentiability of the distance function Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 4 pages The source file(s), CONVEXITYOFCEBYSEVSETSTHROUGHDIFFERENTIABILITYOFDISTANCEFUNCTION.tex: 10884 bytes, is(are) stored in gzipped form as 0810.0587.gz with size 4kb. The corresponding postcript file has gzipped size 41kb. Submitted from: h_haghshenas60@yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0587 or http://arXiv.org/abs/0810.0587 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0587 or in gzipped form by using subject line get 0810.0587 to: math@arXiv.org.