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

In complex analysis, the open mapping theorem states that if U {\displaystyle U} is a domain of the complex plane C {\displaystyle \mathbb {C} } and f...

Open mapping theorem may refer to: Open mapping theorem (functional analysis) (also known as the Banach–Schauder theorem), states that a surjective continuous...

In mathematics, particularly in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological...

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...

fixed-point theorem – Fixed-point theorem for set-valued functions Open mapping theorem (functional analysis) – Condition for a linear operator to be open Ursescu...

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

theorem Open mapping theorem (functional analysis) Product topology Riemann integral Time hierarchy theorem Deterministic time hierarchy theorem Furstenberg's...

theorem (convex analysis) Nash–Moser theorem (mathematical analysis) Open mapping theorem (functional analysis) Peetre theorem (functional analysis)...

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...

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

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...

its inverse is bounded; this follows directly from the open mapping theorem of functional analysis. So, λ is in the spectrum of T if and only if T − λ is...

factorial notation X! may be used for permutations of a single set X. In functional analysis, the same is seen for continuous linear transformations, including...

closed) subsets to open (resp. closed) subsets Open mapping theorem (functional analysis) – Condition for a linear operator to be open (also known as the...

topological vector spaces such that every functional is continuous. On the other hand, the Hahn–Banach theorem, which applies to all locally convex spaces...

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...

plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary...

Ker(T)⊥ → Ran(T) is a bijection, and therefore invertible by the open mapping theorem. Extend this inverse by 0 on Ran(T)⊥ = Ker(T*) to an operator S defined...

Teschl, Gerald (2019). "10. The Brouwer mapping degree". Topics in Linear and Nonlinear Functional Analysis (PDF). Graduate Studies in Mathematics. American...

space to another is an open mapping meaning that it sends open sets to open sets. A corollary is the bounded inverse theorem, that a continuous and bijective...

gradient flow of the Calabi functional; extremal Kähler metrics are the critical points of the Calabi functional. A convergence theorem for the Calabi flow was...

V.} In functional analysis, the open mapping theorem states that every surjective continuous linear operator between Banach spaces is an open map. This...

map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth...

importance of this theorem is related to the open mapping theorem, which states that a continuous linear surjection between Fréchet spaces is an open map. Often...

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

algebra A. The functional calculus can be defined in exactly the same way for an element in A. It is known that the spectral mapping theorem holds for the...

particularly in functional analysis, a webbed space is a topological vector space designed with the goal of allowing the results of the open mapping theorem and the...

important results in functional analysis, like the open mapping theorem, the closed graph theorem, and the Banach–Steinhaus theorem, still hold. Recall...

structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much...