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Surface
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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.
Contents
Definitions and first examples
A (topological) surface is a nonempty
second countable Hausdorff topological space in which every point has an open
neighbourhood mehrSurface aus Wikipedia.
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