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Surface aus Wikipedia. Zum Beitrag

Surface - Wikipedia, the free encyclopedia a.new,#quickbar a.new{color:#ba0000} /* cache key: enwiki:resourceloader:filter:minify-css:3:f2a9127573a22335c2a9102b208c73e7 */ Surface From Wikipedia, the free encyclopedia Jump to: , Look up surface in Wiktionary, the free dictionary. This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X-, Y-, and Z-contours shown. In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 ? for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections. To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian). The concept of surface finds application in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

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Definitions and first examples

A (topological) surface is a nonempty second countable Hausdorff topological space in which every point has an open neighbourhood mehr

Surface aus Wikipedia. Zum Beitrag