Smash Product

In topology, the smash product of two pointed spaces (X, x0) and (Y, y0) is the quotient of the product space X times Y formed by collapsing the subspace consisting of pairs (x, y0) and (x0, y) to a single point, so the resulting basepoint is the equivalence class of (x0, y0). It is usually denoted X wedge Y, and can equivalently be written as the quotient of X times Y by the wedge sum of X and Y. The smash product plays an important role in homotopy theory and algebraic topology, functioning in the category of pointed spaces somewhat like a tensor product.