Abstract
In this paper, we consider the existence of solutions as well as the topological and geometric structure of solution sets for first-order impulsive differential inclusions in some Fréchet spaces. Both the initial and terminal problems are considered. Using ingredients from topology and homology, the topological structures of solution sets (closedness and compactness) as well as some geometric properties (contractibility, acyclicity,
A
R
and
R
δ
) are investigated. Some of our existence results are obtained via the method of taking the inverse system limit on noncompact intervals.