Theorems in topology | Topology
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; Bing gave an alternate proof using in his paper Complementary domains of continuous curves 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. (Wikipedia).
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From playlist Volume and Surface Area
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👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
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👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
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From playlist Mathematics Research Center
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From the Curator: Franz Kline Abstract Expressionist New York The Museum of Modern Art, October 3, 2010--April 11, 2011 MoMA.org/abexny Filmed by Plowshares Media Images courtesy of The Franz Kline Estate; Kate Rothko Prizel & Christopher Rothko; Artists Rights Society (ARS), New Yo
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From playlist MIT 3.091SC Introduction to Solid State Chemistry, Fall 2010
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