Question

Give away the concept of MANIFOLD used in Mathematics.

Answer 1

i donno about that

Answer 2

..Manifold
a mathematical concept that refines and generalizes to any number of dimensions the concept of a curve or surface without singular points (that is, curves without points of self-intersection, end points, and the like and surfaces without self-intersections, boundaries, and so forth).

Examples of one-dimensional manifolds are a line, a parabola, a circle, an ellipse, and, in general, any curve at each point of which there exists a neighborhood that is a one-to-one bicontinuous (or, to use topological terminology, homeomorphic) image of an interval (the interior of a line segment). An interval is itself a one-dimensional manifold, although a line segment is not a manifold, since its end points lack such neighborhoods.

Two-dimensional manifolds include any region in the plane (for example, the interior of the circle x2 + y2 < r2), the plane itself, a paraboloid, a sphere, an ellipsoid, a torus, and others. Each of their points has a neighborhood homeomorphic to the interior of a circle. This requirement eliminates, for example, a conical surface (its vertex, which is common to its two nappes, lacks the type of neighborhood required). However, we distinguish a particular class of objects that do not satisfy this requirement—the manifolds with a boundary (for example, the closed circle x2 + y2 ≤r2).

Three-dimensional manifolds include ordinary Euclidean space as well as any open set in Euclidean space. A characteristic feature of three-dimensional manifolds is that each point of such a manifold has a neighborhood homeomorphic to the interior of a sphere.

Answer 3

http://encyclopedia2.thefreedictionary.com/Manifold+(mathematics)