Remark on Polyhedral Cones a Remark on Polyhedral Cones from Packed Words and from Finite Topologies Darij Grinberg

Definition 0.2. For any two sets X and Y, let Map (X, Y) denote the set of all maps from X to Y. Define a K-vector space M by M = ⊕ n≥0 Map (Rn, K) (where each Map (Rn, K) becomes a K-vector space by pointwise addition and multiplication with scalars). We make M into a K-algebra, whose multiplication is defined as follows: For any n ∈ N, any m ∈ N, any f ∈ Map (Rn, K) and g ∈ Map (Rm, K), we define f g to be the element of Map (Rn+m, K) which sends every (x1, x2, . . . , xn+m) ∈ Rn+m to f (x1, x2, . . . , xn) g (xn+1, xn+2, . . . , xn+m).