We present some results on the existence of mild solutions and study the topological structures of the sets of solutions for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions: $$ \begin{array}{*{20}{c}} {y^{\prime}(t)-A(t)y(t)\in F\left( {t,y(t)} \right)\quad \mathrm{for}\;\mathrm{a}.\mathrm{e}\quad t\in J\backslash \left\{ {{t_1},\ldots,{t_m},\ldots } \right\},} {y\left( {t_k^{+}} \right)-y\left( {t_k^{-}} \right)={I_k}\left( {y\left( {t_k^{-}} \right)} \right),\quad k=1,\ldots,} {y(0)=a} \end{array} $$ and $$ \begin{array}{*{20}{c}} {y^{\prime}(t)-A(t)y(t)\in F\left( {t,y(t)} \right)\quad \mathrm{for}\;\mathrm{a}.\mathrm{e}\quad t\in J\backslash \left\{ {{t_1},\ldots,{t_m},\ldots } \right\},} {y\left( {t_k^{+}} \right)-y\left( {t_k^{-}} \right)={I_k}\left( {y\left( {t_k^{-}} \right)} \right),\quad k=1,\ldots,} {Ly=a,} \end{array} $$ where $ J={{\mathbb{R}}_{+}} $ , 0 = t 0 < t 1 < … < t m <…, $ m\in \mathbb{N} $ , lim k→∞ t k = ∞, A(t) is the infinitesimal generator of a family of evolution operators U(t, s) in a separable Banach space E and F is a set-valued mapping. The functions I k characterize the jumps of solutions at the impulse points t k , k = 1, ….The mapping L: PC b →E is a bounded linear operator. We also investigate the compactness of the set of solutions, some regularity properties of the operator solutions, and the absolute retract.