# wedge product of pointed topological spaces

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]).

## References

• 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.
Title wedge product of pointed topological spaces WedgeProductOfPointedTopologicalSpaces 2013-03-22 18:49:09 2013-03-22 18:49:09 MichaelMcCliment (20205) MichaelMcCliment (20205) 5 MichaelMcCliment (20205) Definition msc 54E99 wedge wedge product QuotientSpace CategoryOfPointedTopologicalSpaces