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

\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
Canonical name	WedgeProductOfPointedTopologicalSpaces
Date of creation	2013-03-22 18:49:09
Last modified on	2013-03-22 18:49:09
Owner	MichaelMcCliment (20205)
Last modified by	MichaelMcCliment (20205)
Numerical id	5
Author	MichaelMcCliment (20205)
Entry type	Definition
Classification	msc 54E99
Synonym	wedge
Synonym	wedge product
Related topic	QuotientSpace
Related topic	CategoryOfPointedTopologicalSpaces