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Surface
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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.

## 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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