In particular, if X and Y are seminormed spaces with seminorms p and q, respectively, then X \otimes_{\pi} Y is a seminormable space whose topology is defined by the seminorm p \otimes q. If (X, p) and (Y, q) are normed spaces then \left(X \otimes Y, p \otimes q\right) is also a normed space, called the projective tensor product of (X, p) and (Y, q), where the topology induced by p \otimes q is the same as the π-topology.
