Local Operation
The connected sum is a local operation on manifolds, meaning that it alters the summands only in a neighborhood of . This implies, for example, that the sum can be carried out on a single manifold containing two disjoint copies of, with the effect of gluing to itself. For example, the connected sum of a two-sphere at two distinct points of the sphere produces the two-torus.
Read more about this topic: Connected Sum
Famous quotes containing the words local and/or operation:
“Savages cling to a local god of one tribe or town. The broad ethics of Jesus were quickly narrowed to village theologies, which preach an election or favoritism.”
—Ralph Waldo Emerson (1803–1882)
“You may read any quantity of books, and you may almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature.”
—Thomas Henry Huxley (1825–95)