wedge product of pointed topological spaces

Definition. Let ${\{(X_i,x_i)\}}_{i\in I}$ be a finite family of disjoint pointed topological spaces. The wedge product of these spaces is

$$\underset{i\in I}{\bigvee }{X}_i=\left(\bigcup _{i\in I}{X}_i\right)/\{x_i:i\in I\}.$$

This can be generalized to arbitrary families of pointed topological spaces, although this may require that the topology on ${\bigcup }_{i\in I}{X}_i$ satisfy a coherence condition (see [1]).