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

$$\bigvee_{i\in I} X_i = \left(\bigcup_{i\in I} X_i\right) / \{x_i: i\in I\}.$$

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]).

Bibliography

1

Munkres, J. R. (2000). Topology (2nd. ed.). Upper Saddle River, NJ: Prentice Hall.

2

Prasolov, V. V. (2004). Elements of combinatorial and differential topology. Providence, RI: American Mathematical Society.

3

Shick, P. L. (2007). Topology: Point-set and geometric. Hoboken, NJ: John Wiley & Sons.