Surface (topology)

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@ Surface (topology)
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Surface (topology)

A surface is a two-dimensional manifold.

n-dimensional manifold, is a topological space with the property that each point has a neighborhood
that is homeomorphic to the Euclidean space of dimension n.

Topological space be defined as a set of points, along with a set of neighborhoods for each point,
satisfying a set of axioms relating points and neighborhoods.

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Surface (math)

A surface is a generalization of a plane, which is not necessarily flat
- that is, the curvature is not necessarily zero.

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The mathematical concept of a surface is an idealization of what is
meant by surface in science, computer graphics, and common language.

Often, a surface is defined by equations that are satisfied by
the coordinates of its points.
This is the case of the graph of a continuous function of two variables.
The set of the zeros of a function of three variables is a surface,
which is called an implicit surface.[1]
If the defining three-variate function is a polynomial,
the surface is an algebraic surface.

A surface may also be defined as the image,
in some space of dimension at least 3, of a continuous function of two variables
(some further conditions are required to insure that the image is not a curve).
In this case, one says that one has a parametric surface, which is
parametrized by these two variables, called parameters.

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