Inside a product space X × Y there are copies of X and Y , namely X × {y 0 } and {x 0 }× Y for points x 0 ∈ X and y 0 ∈ Y . These two copies of X and Y in X × Y intersect only at the point (x 0 , y 0 ) , so their union can be identified with the Wedge sum X ∨ Y . The smash product X ∧ Y is then defined to be the quo- tient X × Y /X ∨ Y . One can think of X ∧ Y as a reduced version of X × Y obtained by collapsing away the parts that are not genuinely a product, the separate factors X and Y . — https://en.wikipedia.org/wiki/Smash_product