Vector space/Mapping set to K/Disjoint union/Exercise

Let ${}K$ be a field, and let ${}I$ denote an index set, together with a partition

${}I=I_{1}\uplus I_{2}\,.$

Show that there exists a natural isomorphism

${}\operatorname {Map} \,{\left(I,K\right)}\cong \operatorname {Map} \,{\left(I_{1},K\right)}\oplus \operatorname {Map} \,{\left(I_{2},K\right)}\,.$

Create a solution