in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely...

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

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

well-known class of closed graph theorems are the closed graph theorems in functional analysis. Definition and notation: The graph of a function f : X...

analysis) Closed graph theorem (functional analysis) Extreme value theorem (calculus) Fixed-point theorems in infinite-dimensional spaces Hairy ball theorem (algebraic...

major theorems which are sometimes called the four pillars of functional analysis: the Hahn–Banach theorem the open mapping theorem the closed graph theorem...

theorem may sometimes be used to show that an extension exists. However, the extension may not be unique. Closed graph theorem (functional analysis) –...

subset. Here, I {\displaystyle I} is the identity operator. By the closed graph theorem, λ {\displaystyle \lambda } is in the spectrum if and only if the...

The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient...

In functional analysis, a branch of mathematics, a closed linear operator or often a closed operator is a linear operator whose graph is closed (see closed...

Robertson–Seymour theorem characterizes minor-closed families as having a finite set of forbidden minors. mixed A mixed graph is a graph that may include...

in functional analysis and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and...

Blumberg theorem guarantees that even this function has some dense subset on which its restriction is continuous. Closed graph theorem (functional analysis) –...

Gregory. Taylor's theorem is taught in introductory-level calculus courses and is one of the central elementary tools in mathematical analysis. It gives simple...

divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through a closed surface to...

In functional analysis, the Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows...

category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure...

In functional analysis, a branch of mathematics, the Hellinger–Toeplitz theorem states that an everywhere-defined symmetric operator on a Hilbert space...

that the graph of a continuous function on a closed interval can be drawn without lifting a pencil from the paper. The intermediate value theorem states...

Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered...

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...

the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional...

its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting...

In functional analysis, a branch of mathematics, a selection theorem is a theorem that guarantees the existence of a single-valued selection function from...

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

the closed graph theorem, which asserts that a linear function from one Banach space to another is continuous if and only if its graph is a closed set...

on the graph converges, its limit point must also belong to the graph. This concept, related to the closed graph property in functional analysis, allows...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

linear operators on a given space are closed. The closed graph theorem asserts that an everywhere-defined closed operator on a complete domain is continuous...

methods from functional analysis, including the Hahn-Banach and Riesz–Markov–Kakutani representation theorems. Cybenko first published the theorem in a technical...