spaces, the closed range theorem gives necessary and sufficient conditions for a closed densely defined operator to have closed range. The theorem was proved...

functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz...

In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives...

analysis) Banach–Steinhaus theorem (functional analysis) Choquet–Bishop–de Leeuw theorem (functional analysis) Closed range theorem (functional analysis) Dunford–Schwartz...

Steinhaus said of Banach: "Banach was my greatest scientific discovery." Closed range theorem International Stefan Banach Prize List of Poles List of Polish mathematicians...

Brouwer's theorem are for continuous functions f {\displaystyle f} from a closed interval I {\displaystyle I} in the real numbers to itself or from a closed disk...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R 2...

the Artin–Schreier theorem states that F has an algebraic extension, called the real closure K of F, such that K is a real closed field whose ordering...

closed and bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is...

who proved it first in 1930 for powers of the closed unit interval and in 1935 stated the full theorem along with the remark that its proof was the same...

of the so-called closed range theorem.) In particular, T has closed range if and only if T ∗ {\displaystyle T^{*}} has closed range. In contrast to the...

on a closed interval can be drawn without lifting a pencil from the paper. The intermediate value theorem states the following: Consider the closed interval...

finite-dimensional Euclidean spaces, is generalized by the Krein–Smulian theorem, according to which the closed convex hull of a weakly compact subset of a Banach space...

finite-dimensional (where T* denotes the adjoint of T), and the range Ran(T) is closed. Atkinson's theorem states: A T ∈ L(H) is a Fredholm operator if and only...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

the closed graph theorem for set-valued functions, which says that for a compact Hausdorff range space Y, a set-valued function φ: X→2Y has a closed graph...

In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued...

stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

measures, Lyapunov's theorem states that the range of a (non-atomic) finite-dimensional vector measure is closed and convex. In fact, the range of a non-atomic...

the Whitney extension theorem is a partial converse to Taylor's theorem. Roughly speaking, the theorem asserts that if A is a closed subset of a Euclidean...

  A closed operator is a linear operator whose graph is closed. 3.  The closed range theorem says that a densely defined closed operator has closed image...

receives. Voters may cast votes for parties, as in Spain, Turkey, and Israel (closed lists); or for candidates whose vote totals are pooled together to parties...

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with...

reals, Sturm's theorem is less efficient than other methods based on Descartes' rule of signs. However, it works on every real closed field, and, therefore...

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations...

mathematical fields of topology and K-theory, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic...