We investigate the AR-property for convex sets in nonlocally convex linear metric spaces. We introduce the notion of LC-decomposability for convex sets and prove that any LC-decomposable convex set is an AR.
"LC-decomposability and the AR-properly in linear metric spaces." Tsukuba J. Math. 21 (1) 117 - 128, June 1997. https://doi.org/10.21099/tkbjm/1496163165