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:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.”
—Francis Bacon (1560–1626)