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A space of functions comprising a complete biorthogonal system.

A set in R^d is concave if it does not contain all the line segments connecting any pair of its points. If the set does contain all the line segments, it is called convex.

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

A continuous map is a continuous function between two topological spaces. In some fields of mathematics, the term "function" is reserved for functions which are into the real ...

A set X is a called a "convex cone" if for any x,y in X and any scalars a>=0 and b>=0, ax+by in X.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

Suppose that X^~,X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~,p) is said to be a covering space of X if p:X^~->X is a surjective ...

A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.