The wedge sum of based spaces is their disjoint union with all basepoints identified, equipped with the quotient topology. It is the coproduct
in the category of based spaces. For two spaces it is
denoted by 
.
Two circles joined at their basepoints give a figure-eight space. The inclusion 
is used in defining
the smash product. For spectra,
a finite wedge is also a direct
sum, whereas a filtration by specified cofibers need
not split as their wedge.
Wedge Sum
See also
Cofiber, Smash Product, Topological SpectrumExplore with Wolfram|Alpha
References
Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Cite this as:
Weisstein, Eric W. "Wedge Sum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WedgeSum.html