Examples
The wedge sum of two circles is homeomorphic to a figure-eight space. The wedge sum of n circles is often called a bouquet of circles, while a wedge product of arbitrary spheres is often called a bouquet of spheres.
A common construction in homotopy is to identify all of the points along the equator of an n-sphere . Doing so results in two copies of the sphere, joined at the point that was the equator:
Let be the map, that is, of identifying the equator down to a single point. Then addition of two elements of the n-dimensional homotopy group of a space X at the distinguished point can be understood as the composition of and with :
Here, and are understood to be maps, and similarly for, which take a distinguished point to a point . Note that the above defined the wedge sum of two functions, which was possible because, which was the point that is equivalenced in the wedge sum of the underlying spaces.
Read more about this topic: Wedge Sum
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)