Aronszajn-Hukuhara type theorem for semilinear differential inclusions with nonlocal conditions

In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that the mild solution set is a compact absolute retract (and then a continuum and $R_delta$-set). As a particular case, the topological structure of the periodic mild solution set is deduced. An illustrating example is supplied.