Search Results for ""

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

A metric space X is isometric to a metric space Y if there is a bijection f between X and Y that preserves distances. That is, d(a,b)=d(f(a),f(b)). In the context of ...

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

Let (X,tau) be a topological space, and let p in X. Then the arc component of p is union {A subset= X:A is an arc and p in A}.

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

A family of subsets of a topological space such that every point has a neighborhood that intersects only one of them.