Abstract
In this paper, we investigate the following question in a general setting: For a multi-valued mapping F on a Banach space X, when does dimF(x) >= n imply dimFix(F) >= n, where dimF(x) and dimFix(F) denote the topological (covering) dimension of F(x) and the fixed points set Fix(F) of F respectively? We apply our results to the solution set of a Cauchy problem for the fractional differential inclusion with nonlocal condition.