Surface::surfaces    Which::closed    Sphere::space    Boundary::plane    Torus::compact    '''P'''::complex


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, such as a sphere. 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.



Surface sections
Intro  Definitions and first examples  Extrinsically defined surfaces and embeddings  Construction from polygons  Connected sums   Closed surfaces   Surfaces in geometry  See also  Notes  References  External links  

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