User contributions for Anghel
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3 February 2023
- 16:2916:29, 3 February 2023 diff hist +57 Connected and Locally Path-Connected Implies Path Connected Might need to make this proof clearer.
- 16:2716:27, 3 February 2023 diff hist +1,648 N Path Component of Locally Path-Connected Space is Closed Created page with "== Theorem == Let $T = \left({S, \tau}\right)$ be a locally path-connected topological space. Let $G$ be a path component of $T$. Then $G$ is open in $T$. == Proof == Let $x \in \partial G$, where $\partial G$ denotes the boundary of $G$. By {{Open-set-axiom|3}}, it follows that..."
- 16:1816:18, 3 February 2023 diff hist +11 m Definition:Boundary (Topology)/Definition 2 No edit summary
31 January 2023
- 13:2713:27, 31 January 2023 diff hist −35 m Gödel's Incompleteness Theorems/Second Reverted edits by DVD (talk) to last revision by Prime.mover Tag: Rollback
30 January 2023
- 22:0422:04, 30 January 2023 diff hist +106 Pi is Irrational/Proof 1 Just added three links
- 17:0417:04, 30 January 2023 diff hist +204 User:Anghel/Projects No edit summary current
- 16:3016:30, 30 January 2023 diff hist 0 Book:Christian Berg/Mål- og integralteori No edit summary current
- 16:3016:30, 30 January 2023 diff hist +219 Book:Christian Berg/Mål- og integralteori No edit summary
- 16:2616:26, 30 January 2023 diff hist +273 Book:Christian Berg/Metriske rum No edit summary current
- 16:0516:05, 30 January 2023 diff hist +21 ProofWiki:Potw No edit summary
- 16:0416:04, 30 January 2023 diff hist +11 Laplace Transform of Complex Power No edit summary
- 16:0316:03, 30 January 2023 diff hist +7 Pi is Irrational/Proof 1 No edit summary
- 16:0116:01, 30 January 2023 diff hist +11 Pi is Irrational/Proof 1 No edit summary
29 January 2023
- 20:5120:51, 29 January 2023 diff hist +172 Mathematician:Christian Berg No edit summary
- 20:4820:48, 29 January 2023 diff hist +639 N Book:Christian Berg/Mål- og integralteori Created page with "{{Book|Mål- og integralteori|2001|Universitetsbogladen|87-7834-424-7|Christian Berg|Tage Gutmann Madsen}} This book is based on a set of notes originally written in 1970 by Tage Gutmann Madsen to be used at the basic course about measure theory at the University of Copenhagen. === Subject Matter === * Measure Theory == Download == The book can be downloaded as a PDF..."
- 20:4120:41, 29 January 2023 diff hist +539 N Book:Christian Berg/Metriske rum Created page with "{{Book|Metriske rum|1997|Universitetsbogladen|87-91180-01-5|Christian Berg}} This book is based on a set of notes written in 1990 by the author to be used at the basic course about metric spaces at the University of Copenhagen. === Subject Matter === * Metric Spaces == Download == The book can be downloaded as a PDF file from the University of Copenhagen for free. [https://web.math.ku.dk/noter/filer/matemati..."
- 14:2914:29, 29 January 2023 diff hist +101 Definition:Symmetric Bilinear Form/Nondegenerate No edit summary
- 14:2814:28, 29 January 2023 diff hist −1 Definition:Inner Product Space No edit summary
- 14:2814:28, 29 January 2023 diff hist +544 Definition:Inner Product Space No edit summary
- 14:1614:16, 29 January 2023 diff hist +203 Definition:Inner Product/Also known as No edit summary
- 14:1214:12, 29 January 2023 diff hist +114 Definition:Inner Product/Real Field No edit summary
- 14:1114:11, 29 January 2023 diff hist +114 Definition:Inner Product/Complex Field No edit summary
- 14:0914:09, 29 January 2023 diff hist +794 N Definition:Inner Product/Also defined as Created page with "== Also defined as == Let $V$ be a vector space over a field $\GF$ that is a subfield of $\R$ or $\C$. Let $\innerprod \cdot \cdot: V \times V \to \GF$ be an inner product on $\GF$. <onlyinclude> Some texts define an '''inner product''' only for vector spaces over $\R$ or $\C$. This ensures that for all $v \in V$, the Definition:Inner Pr..."
- 14:0614:06, 29 January 2023 diff hist −10 Definition:Inner Product No edit summary
- 13:5913:59, 29 January 2023 diff hist +302 Definition:Scalar Product No edit summary current
- 13:5313:53, 29 January 2023 diff hist +266 Definition:Scalar Product Space No edit summary
28 January 2023
- 22:2622:26, 28 January 2023 diff hist +386 Definition talk:Nondegenerate Tuple of Elements of Scalar Product Space No edit summary
- 22:0822:08, 28 January 2023 diff hist +103 N Definition:Nondegenerate Symmetric Bilinear Form This clears 6 red links. Tag: New redirect
- 22:0522:05, 28 January 2023 diff hist +547 N Definition:Symmetric Bilinear Form/Nondegenerate Created page with "== Definition == <onlyinclude> Let $\Bbb K$ be a field. Let $V$ be a vector space over $\Bbb K$. Let $b: V \times V \to \Bbb K$ be a symmetric bilinear form. Let $b$ be a nondegenerate bilinear form. Then $b$ is a '''nondegenerate symmetric bilinear form'''. </onlyinclude> == Sources == * {{MathWorld|Symmetric Biline..."
- 21:5921:59, 28 January 2023 diff hist +233 Definition:Symmetric Bilinear Form No edit summary
- 21:2721:27, 28 January 2023 diff hist −8 Definition:Orthogonal (Linear Algebra)/Orthogonal Complement No edit summary current
- 21:2621:26, 28 January 2023 diff hist −8 Definition:Isometry (Inner Product Spaces) No edit summary current
- 21:2521:25, 28 January 2023 diff hist −8 Definition:Orthonormal Subset No edit summary current
- 21:2421:24, 28 January 2023 diff hist +1 Gram-Schmidt Orthogonalization/Corollary 2 No edit summary current
- 21:2021:20, 28 January 2023 diff hist 0 m Gram-Schmidt Orthogonalization/Corollary 2 Anghel moved page Gram-Schmidt Orthogonalization/Inner Product Space to Gram-Schmidt Orthogonalization/Corollary 2 without leaving a redirect
- 21:1921:19, 28 January 2023 diff hist +140 Gram-Schmidt Orthogonalization No edit summary
- 21:1821:18, 28 January 2023 diff hist +18 Gram-Schmidt Orthogonalization/Corollary 1 No edit summary current
- 21:1721:17, 28 January 2023 diff hist 0 m Talk:Gram-Schmidt Orthogonalization/Corollary 1 Anghel moved page Talk:Gram-Schmidt Orthogonalization/Corollary to Talk:Gram-Schmidt Orthogonalization/Corollary 1 without leaving a redirect: Room for more corollaries current
- 21:1721:17, 28 January 2023 diff hist 0 m Gram-Schmidt Orthogonalization/Corollary 1 Anghel moved page Gram-Schmidt Orthogonalization/Corollary to Gram-Schmidt Orthogonalization/Corollary 1 without leaving a redirect: Room for more corollaries
- 21:1721:17, 28 January 2023 diff hist −353 Gram-Schmidt Orthogonalization/Corollary 2 Merging in process
- 21:0321:03, 28 January 2023 diff hist +1,687 Definition talk:Inner Product No edit summary
- 20:1720:17, 28 January 2023 diff hist +263 Definition talk:Nondegenerate Tuple of Elements of Scalar Product Space No edit summary
- 16:2516:25, 28 January 2023 diff hist +1,892 Definition talk:Inner Product No edit summary
- 15:5715:57, 28 January 2023 diff hist +1,598 Definition talk:Nondegenerate Tuple of Elements of Scalar Product Space No edit summary
27 January 2023
- 21:3521:35, 27 January 2023 diff hist +49 User:Anghel/Projects No edit summary
- 20:2320:23, 27 January 2023 diff hist +3 Union of Simply Connected Sets with Path-Connected Intersection is Simply Connected No edit summary current
- 18:3718:37, 27 January 2023 diff hist −23 m Cartesian Product of Intervals is Simply Connected No edit summary current
- 18:0418:04, 27 January 2023 diff hist +879 N Union of Simply Connected Sets with Path-Connected Intersection is Simply Connected Created page with "== Theorem == Let $\struct {T, \tau}$ be a topological space. Consider all subsets of $T$ as subspaces, equipped with the subspace topology induced by $T$. Let $U$ and $V$ be open subsets of $T$ that are simply connected. Let $U \cap V$ be Definition:Non-Empty Set|no..."
- 16:1816:18, 27 January 2023 diff hist +773 N Cartesian Product of Intervals is Simply Connected Created page with "== Theorem == Let $n \in \N$. For all $k \in \set {1, \ldots, n}$, let $\Bbb I_k$ be a real interval of any of the real interval types. Let $\tau_0$ denote the subspace topology on the cartesian product $\Bbb I_1 \times \ldots \times \Bbb I_n$, induced by the Euclidean topology on $\R..."
- 16:1216:12, 27 January 2023 diff hist +1,692 N Cartesian Product of Intervals is Convex Set Created page with "== Theorem == Let $n \in \N$. For all $k \in \set {1, \ldots, n}$, let $\Bbb I_k$ be a real interval of any of the real interval types. Then the cartesian product $\Bbb I_1 \times \ldots \times \Bbb I_n$ is a convex set. == Proof == Let $\mathbf x, \mathbf y \in \Bbb I_1 \times \ldots \times \Bbb I_n$ with: {{begin-eqn}} {{eqn..." current