open mapping
81Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… …
82Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …
83Functional analysis — For functional analysis as used in psychology, see the functional analysis (psychology) article. Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon… …
84Uniform boundedness principle — In mathematics, the uniform boundedness principle or 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 one of the cornerstones… …
85List of mathematical proofs — A list of articles with mathematical proofs:Theorems of which articles are primarily devoted to proving them: See also: *Bertrand s postulate and a proof *Estimation of covariance matrices *Fermat s little theorem and some proofs *Gödel s… …
86List of functional analysis topics — This is a list of functional analysis topics, by Wikipedia page. Contents 1 Hilbert space 2 Functional analysis, classic results 3 Operator theory 4 Banach space examples …
87Rouché's theorem — In mathematics, especially complex analysis, Rouché s theorem tells us that if the complex valued functions f and g are holomorphic inside and on some closed contour C , with | g ( z )| < | f ( z )| on C , then f and f + g have the same number of …
88Atkinson's theorem — In operator theory, Atkinson s theorem gives a characterization of Fredholm operators. The theorem Let H be a Hilbert space and L ( H ) the bounded operators on H . The following is the classical definition of a Fredholm operator: a T ∈ L ( H )… …
89Bounded inverse theorem — In mathematics, the bounded inverse theorem is a result in the theory of bounded linear operators on Banach spaces. It states that a bijective bounded linear operator T from one Banach space to another has bounded inverse T −1. It is equivalent… …
90Théorème de l'application ouverte (analyse complexe) —  Ne pas confondre ce théorème ci de l application ouverte avec cet autre : théorème de Banach Schauder. En mathématiques, et plus précisément en analyse complexe, le théorème de l application ouverte affirme que les fonctions… …
