It is also somewhat common to write
\[ X\wedge Y\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\frac{X\times Y}{X\vee Y}, \]
identifying $X\vee Y$ with the subspace $\webleft (\webleft\{ x_{0}\webright\} \times Y\webright )\cup \webleft (X\times \webleft\{ y_{0}\webright\} \webright )$ of $X\times Y$, and having the quotient be defined by declaring $\webleft (x,y\webright )\sim \webleft (x',y'\webright )$ iff we have $\webleft (x,y\webright ),\webleft (x',y'\webright )\in X\vee Y$.
