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]).
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 |