In mathematics, a Kline sphere characterization, named after John Robert Kline, is a topological characterization of a two-dimensional sphere in terms of what sort of subset separates it. Its proof was one of the first notable accomplishments of R.H. Bing.
A simple closed curve in a two-dimensional sphere (for instance, its equator) separates the sphere into two pieces upon removal. If one removes a pair of points from a sphere, however, the remainder is connected. Kline's sphere characterization states that the converse is true: If a nondegenerate locally connected metric continuum is separated by any simple closed curve but by no pair of points, then it is a two-dimensional sphere.
Famous quotes containing the word sphere:
“If today there is a proper American “sphere of influence” it is this fragile sphere called earth upon which all men live and share a common fate—a sphere where our influence must be for peace and justice.”
—Hubert H. Humphrey (1911–1978)