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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topology, the closed graph theorem is a result connecting the continuity of certain kinds of functions to a topological property of their graph. In its most...
25 KB (4,753 words) - 22:04, 18 March 2023
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 (2,736 words) - 13:56, 25 March 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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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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closed graph theorem). Local convexity of X {\displaystyle X} or Y {\displaystyle Y} is not essential to the proof, but completeness is: the theorem...
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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...
35 KB (4,471 words) - 04:49, 30 April 2024
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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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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inverse T−1. It is equivalent to both the open mapping theorem and the closed graph theorem. Theorem — If A : X → Y is a continuous linear bijection from...
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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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Hemicontinuity (section Closed graph theorem)
} has open lower sections then it is lower hemicontinuous. The open graph theorem says that if Γ : A → P ( R n ) {\displaystyle \Gamma :A\to P\left(\mathbb...
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to the graph of the function) is zero. The theorem is named after Michel Rolle. If a real-valued function f is continuous on a proper closed interval...
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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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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...
106 KB (15,667 words) - 12:01, 16 May 2024
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...
35 KB (4,046 words) - 19:56, 14 January 2024
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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ISSN 0032-5155. Retrieved 20 May 2024. ——— (1978). "The range space in a closed graph theorem". Acta Mathematica Academiae Scientiarum Hungaricae. 32 (1–2). Springer...
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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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In topology, the Jordan curve theorem asserts that every Jordan curve (a plane simple closed curve) divides the plane into an "interior" region bounded...
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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...
48 KB (6,275 words) - 02:20, 28 April 2024
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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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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the Blumberg theorem guarantees that even this function has some dense subset on which its restriction is continuous. Closed graph theorem (functional...
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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...
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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...
8 KB (939 words) - 09:38, 2 June 2023
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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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...
30 KB (5,658 words) - 01:03, 18 April 2024
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...
67 KB (7,988 words) - 11:39, 14 May 2024
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...
15 KB (2,572 words) - 13:00, 26 June 2023