mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions...
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the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem states...
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function with a closed graph is necessarily continuous. One particularly well-known class of closed graph theorems are the closed graph theorems in functional...
22 KB (2,976 words) - 17:03, 20 July 2024
and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle...
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The closed graph theorem says a linear operator between Banach spaces is a closed operator if and only if it is a bounded operator. Hence, a closed linear...
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Functional analysis (section Closed graph theorem)
major theorems which are sometimes called the four pillars of functional analysis: the Hahn–Banach theorem the open mapping theorem the closed graph theorem...
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redirect targets Closed graph theorem – Theorem relating continuity to graphs Closed graph theorem (functional analysis) – Theorems connecting continuity...
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graph theory, the Robertson–Seymour theorem (also called the graph minor theorem) states that the undirected graphs, partially ordered by the graph minor...
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spaces) and φ is required to be closed-valued in the alternative statement of the Kakutani theorem, the Closed Graph Theorem implies that the two statements...
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whether any minor-closed class of graphs is determined by a finite set of "forbidden minors". This is now the Robertson–Seymour theorem, proved in a long...
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Hamiltonian path (redirect from Hamiltonian graph)
Ore's theorems basically state that a graph is Hamiltonian if it has enough edges. The Bondy–Chvátal theorem operates on the closure cl(G) of a graph G with...
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complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and...
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Hemicontinuity (section Closed graph theorem)
graph of Γ {\displaystyle \Gamma } is the set of all a ∈ A {\displaystyle a\in A} such that Γ ( a ) {\displaystyle \Gamma (a)} is not empty. Theorem — If...
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2-factor theorem (graph theory) 15 and 290 theorems (number theory) 2π theorem (Riemannian geometry) AF+BG theorem (algebraic geometry) ATS theorem (number...
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The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the complete...
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Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph theorem...
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topology, the Jordan curve theorem, formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the plane...
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planar graph can be formed from a map in this way. In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can...
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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...
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Otto Toeplitz. This theorem can be viewed as an immediate corollary of the closed graph theorem, as self-adjoint operators are closed. Alternatively, it...
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Webbed space (section Theorems)
with the goal of allowing the results of the open mapping theorem and the closed graph theorem to hold for a wider class of linear maps whose codomains...
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the graph). The second example illustrates the following generalization of Rolle's theorem: Consider a real-valued, continuous function f on a closed interval...
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is used in functional analysis to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle. BCT1 also shows that...
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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...
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graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...
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doi:10.1007/BF01896945. ISSN 0001-5954. ——— (1968). "-spaces and the closed-graph theorem". Proceedings of the Edinburgh Mathematical Society. 16 (2). Cambridge...
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In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite...
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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...
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theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of...
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Continuous linear extension (redirect from BLT-theorem)
Hahn–Banach theorem may sometimes be used to show that an extension exists. However, the extension may not be unique. Closed graph theorem (functional...
4 KB (741 words) - 23:44, 28 January 2023