# User contributions for Usagiop

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- 21:07, 8 August 2022 diff hist −6 Definition:Ergodic Measure-Preserving Transformation/Definition 4 current
- 21:02, 8 August 2022 diff hist +388 Equivalence of Defintions of Ergodic Measure-Preserving Transformation current
- 20:54, 8 August 2022 diff hist +194 Equivalence of Defintions of Ergodic Measure-Preserving Transformation Add assumption
- 20:25, 8 August 2022 diff hist 0 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 20:23, 8 August 2022 diff hist +27 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 20:21, 8 August 2022
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**+629** Equivalence of Defintions of Ergodic Measure-Preserving Transformation Add proof from 3 to 4 - 23:36, 7 August 2022 diff hist +382 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:28, 7 August 2022 diff hist +11 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:27, 7 August 2022 diff hist +102 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:25, 7 August 2022 diff hist +320 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:16, 7 August 2022
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**+524** Equivalence of Defintions of Ergodic Measure-Preserving Transformation - 23:11, 7 August 2022 diff hist +85 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:09, 7 August 2022 diff hist 0 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:08, 7 August 2022 diff hist +7 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 23:06, 7 August 2022 diff hist +195 Equivalence of Defintions of Ergodic Measure-Preserving Transformation
- 22:57, 7 August 2022
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**+717** Equivalence of Defintions of Ergodic Measure-Preserving Transformation Add a partial proof - 22:20, 7 August 2022
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**+996** N Equivalence of Defintions of Ergodic Measure-Preserving Transformation Created page with "== Theorem == {{TFAE|def = Ergodic Measure-Preserving Transformation}} === Definition 1 === {{Definition:Ergodic Measure-Preserving Transformation/Definition 1}} === Definition 2 === {{Definition:Ergodic Measure-Preserving Transformation/Definition 2}} === Definition:Ergodic Measure-Preserving Transformation/Definition 3|Defini..." - 08:25, 6 August 2022 diff hist −75 Zero Locus of Vanishing Ideal is Closure current
- 23:18, 5 August 2022 diff hist +1 m Definition:Quasi-Affine Variety
- 23:18, 5 August 2022
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**+623** N Definition:Quasi-Affine Variety Created page with "== Definition == Let $k$ be a field. Let $n \ge 1$ be an Integer. Let $k^n$ be equipped with Zariski topology. Then a subset $Y \subseteq k^n$ is an '''quasi-affine variety''' if $Y$ is a open set of an affine variety. == Sources == * {{BookReference|Algebraic G..." - 23:13, 5 August 2022 diff hist +65 Definition:Affine Algebraic Variety current
- 18:04, 5 August 2022 diff hist 0 Definition:Affine Algebraic Variety
- 07:59, 5 August 2022 diff hist +1 m Definition:Standard Affine Space
- 07:58, 5 August 2022 diff hist −5 Definition:Standard Affine Space
- 07:57, 5 August 2022 diff hist +64 Definition:Standard Affine Space
- 07:56, 5 August 2022 diff hist +99 Definition:Standard Affine Space
- 07:53, 5 August 2022 diff hist 0 Definition:Standard Affine Space
- 07:52, 5 August 2022 diff hist +53 Definition:Affine Algebraic Variety
- 07:46, 5 August 2022 diff hist +108 Definition:Affine Algebraic Variety
- 23:20, 2 August 2022 diff hist +4 m Definition:Affine Coordinate Ring
- 23:18, 2 August 2022 diff hist +17 m Definition:Affine Coordinate Ring
- 23:17, 2 August 2022 diff hist +91 Definition:Affine Coordinate Ring
- 23:14, 2 August 2022 diff hist +4 m Definition:Affine Coordinate Ring
- 23:13, 2 August 2022 diff hist +1 m Definition:Affine Coordinate Ring
- 23:12, 2 August 2022 diff hist +38 Definition:Affine Coordinate Ring
- 23:11, 2 August 2022 diff hist +47 Definition:Affine Coordinate Ring
- 23:10, 2 August 2022 diff hist +3 Definition:Affine Coordinate Ring
- 23:09, 2 August 2022
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**+615** N Definition:Affine Coordinate Ring Created page with "== Definition == Let $k$ be a field. Let $Y \subseteq k^n$ be an affine algebraic set. Then '''affine coordinate ring''' of $Y$ is defined as :$\map A Y := k \sqbrk {X_1, \ldots, X_n}/\map I Y$ where: :$k \sqbrk {X_1, \ldots, X_n}$ is the polynomial ring in $n$ variables over $k$ :$\map I Y$ is the Definition:Vanishing Ideal of Subset of..." - 22:17, 2 August 2022 diff hist +158 Vanishing Ideal of Larger Subset of Affine Space is Smaller current
- 20:19, 1 August 2022 diff hist +41 m Power Series is Termwise Differentiable within Radius of Convergence current
- 20:18, 1 August 2022 diff hist +40 Power Series is Termwise Differentiable within Radius of Convergence
- 20:16, 1 August 2022 diff hist +22 Power Series is Termwise Differentiable within Radius of Convergence
- 20:13, 1 August 2022 diff hist +91 Power Series is Termwise Differentiable within Radius of Convergence
- 20:37, 28 July 2022
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**+711** N Zero Locus of Vanishing Ideal is Closure Created page with "== Theorem == Let $k$ be a field. Let $n \ge 1$ be a natural number. Let $\mathbb A^n_k$ be the standard affine space over $k$. Let $S \subseteq \mathbb A^n_k$. Let $S^-$ be the closure of $S$ with respect to Zariski topology. Then: :$\map V {\map I S} = S^-$ where: :$\map I \cdot..." - 20:30, 28 July 2022
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**+783** N Vanishing Ideal of Zero Locus of Ideal is Radical Created page with "== Theorem == Let $k$ be a field. Let $n \ge 1$ be a natural number. Let $k \sqbrk {X_1, \ldots, X_n}$ be the polynomial ring in $n$ variables over $k$. Let $\mathfrak a \subseteq k \sqbrk {X_1, \ldots, X_n}$ be an ideal. Then: :$\map I {\map V {\mathfrak a} } = \map \Rad {\mathfrak a}$ where: :$\map V \cdot$ denot..." current - 15:53, 28 July 2022 diff hist +50 Closed Unit Ball is Convex Set
- 09:48, 28 July 2022 diff hist 0 m Diagonalizable Operator Bounded iff Value Set Bounded current
- 09:47, 28 July 2022 diff hist −11 Diagonalizable Operator Bounded iff Value Set Bounded
- 09:03, 28 July 2022 diff hist +50 Definition:Standard Affine Space
- 08:59, 28 July 2022 diff hist +4 m Vanishing Ideal of Larger Subset of Affine Space is Smaller