User contributions for Leigh.Samphier
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- 12:50, 23 June 2022 diff hist +106 User:Leigh.Samphier/Refactor current
- 12:32, 23 June 2022 diff hist +28 User:Leigh.Samphier/Refactor
- 12:31, 23 June 2022 diff hist +43 User:Leigh.Samphier/Refactor
- 12:29, 23 June 2022 diff hist +39 User:Leigh.Samphier/Refactor
- 12:27, 23 June 2022 diff hist +32 User:Leigh.Samphier/Refactor
- 12:01, 23 June 2022 diff hist +75 User:Leigh.Samphier/Refactor
- 11:52, 23 June 2022 diff hist −140 User:Leigh.Samphier/Refactor
- 11:48, 23 June 2022 diff hist −1,706 Norm of Vector Cross Product current
- 11:41, 23 June 2022 diff hist 0 m Square of Norm of Vector Cross Product Leigh.Samphier moved page User:Leigh.Samphier/Refactor/Square of Norm of Vector Cross Product to Square of Norm of Vector Cross Product
- 11:40, 23 June 2022 diff hist +1,756 N Square of Norm of Vector Cross Product Created page with "== Theorem == Let $\mathbf a$ and $\mathbf b$ be vectors in the Euclidean space $\R^3$. Let $\times$ denote the vector cross product. Then: :$\norm{ \mathbf a \times \mathbf b }^2 = \norm{\mathbf a}^2 \norm{\mathbf b}^2 - \paren{\mathbf a \cdot \mathbf b}^2$ == Proof == Let $\mathbf a = \begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix}$, and $\mathbf b = \..."
- 11:16, 23 June 2022 diff hist +104 User:Leigh.Samphier/Refactor
- 10:44, 23 June 2022 diff hist +1 User:Leigh.Samphier/Templates/CommonHeader current
- 08:10, 23 June 2022 diff hist +157 User:Leigh.Samphier/Templates/CommonHeader
- 22:29, 22 June 2022 diff hist +51 User:Leigh.Samphier current
- 22:28, 22 June 2022 diff hist −225 User:Leigh.Samphier/Refactor
- 22:27, 22 June 2022 diff hist +357 N User:Leigh.Samphier/Refactor Created page with "{{:User:Leigh.Samphier/Templates/CommonHeader}} == Refactor == ::Equivalence of Definitions of Compact Topological Space ::Sequence Lemma ::Countable Product of Sequentially Compact Spaces is Sequentially Compact ::Sequence Characterization of Open Sets ::Final Topology with respect to Mapping"
- 21:58, 22 June 2022 diff hist +33 User:Leigh.Samphier/Topology current
- 21:11, 22 June 2022 diff hist +145 Every Filter has Limit Point implies Every Ultrafilter Converges current
- 20:57, 22 June 2022 diff hist +1 Compactness from Basis current
- 20:56, 22 June 2022 diff hist −9 Equivalence of Definitions of Compact Topological Space current
- 20:55, 22 June 2022 diff hist +1,017 Compactness from Basis
- 20:20, 22 June 2022 diff hist +236 Equivalence of Definitions of Compact Topological Space
- 20:16, 22 June 2022 diff hist −35 Compactness from Basis
- 20:07, 22 June 2022 diff hist +557 N Definition:Compact Space/Topology/Definition 6 Created page with "== Definition == <onlyinclude> A topological space $T = \struct {S, \tau}$ is '''compact''' {{iff}} $\tau$ has a basis $\BB$ such that: :from every cover of $S$ by elements of $\BB$, a finite subcover of $S$ can be selected. </onlyinclude> == Also see == * Equivalence of Definitions of Compact Topological Space {{LinkTo..."
- 19:20, 22 June 2022 diff hist +8 Definition:Compact Space/Euclidean Space current
- 19:12, 22 June 2022 diff hist +45 Pasting Lemma/Pair of Continuous Mappings on Open Sets/Proof 2
- 19:12, 22 June 2022 diff hist +45 Pasting Lemma/Pair of Continuous Mappings on Open Sets/Proof 1
- 19:11, 22 June 2022 diff hist +72 Pasting Lemma/Pair of Continuous Mappings on Open Sets
- 19:11, 22 June 2022 diff hist +1 Category:Pasting Lemma for Pair of Continuous Mappings on Open Sets
- 19:11, 22 June 2022 diff hist +143 N Category:Pasting Lemma for Pair of Continuous Mappings on Open Sets Created page with "{{SubjectCategory|result = Pasting Lemma for Pair of Continuous Mappings on Open Sets}} Category:Open Sets Category:Continuous Mapping"
- 19:08, 22 June 2022 diff hist −1,500 Pasting Lemma/Pair of Continuous Mappings on Open Sets
- 19:06, 22 June 2022 diff hist +1,795 N Pasting Lemma/Pair of Continuous Mappings on Open Sets/Proof 2 Created page with "== Theorem == {{:Pasting Lemma/Pair of Continuous Mappings on Open Sets}} == Proof == <onlyinclude> From Union of Mappings which Agree is Mapping :$f \cup g$ is well-defined. By {{Defof|Continuous Mapping}}: :$f \cup g$ is continuous {{iff}} $\paren {f \cup g}^{-1} \sqbrk U$ is open in $A \cup B$ for every open $U$ in $..."
- 19:05, 22 June 2022 diff hist +229 N Pasting Lemma/Pair of Continuous Mappings on Open Sets/Proof 1 Created page with "== Theorem == {{:Pasting Lemma/Pair of Continuous Mappings on Open Sets}} == Proof == <onlyinclude> Follows directly from Pasting Lemma for Continuous Mappings on Open Sets. {{qed}}</onlyinclude> Category:Pasting Lemma"
- 16:50, 22 June 2022 diff hist −82 User:Leigh.Samphier/Topology Tag: Manual revert
- 16:49, 22 June 2022 diff hist −1,500 Pasting Lemma/Pair of Continuous Mappings on Open Sets
- 16:42, 22 June 2022 diff hist 0 m Preimage of Union Mapping is Union of Preimages Leigh.Samphier moved page User:Leigh.Samphier/Topology/Preimage of Union Mapping is Union of Preimages to Preimage of Union Mapping is Union of Preimages current
- 16:41, 22 June 2022 diff hist +1 Preimage of Union Mapping is Union of Preimages
- 16:41, 22 June 2022 diff hist +1 Preimage of Union Mapping is Union of Preimages
- 16:40, 22 June 2022 diff hist +15 Preimage of Union Mapping is Union of Preimages
- 16:39, 22 June 2022 diff hist 0 Preimage of Union Mapping is Union of Preimages
- 16:39, 22 June 2022 diff hist +1 Preimage of Union Mapping is Union of Preimages
- 16:38, 22 June 2022 diff hist +1 Preimage of Union Mapping is Union of Preimages
- 16:38, 22 June 2022 diff hist +110 Preimage of Union Mapping is Union of Preimages
- 16:36, 22 June 2022 diff hist +1,760 N Preimage of Union Mapping is Union of Preimages Created page with "== Theorem == <onlyinclude> Let $A$, $B$ and $Y$ be sets. Let $f: A \to Y$ and $g: B \to Y$ be mappings that agree on $A \cap B$. Let $f \cup g$ be the union of the mappings $f$ and $g$: :$\forall x \in A \cup B: \map {f \cup g} x = \begin {cases} \map f x & : x \in A \\ \map g x & : x \in B \end {cases}$ Let $S \subseteq Y$ be a Definition..."
- 16:27, 22 June 2022 diff hist +82 User:Leigh.Samphier/Topology Tag: Reverted
- 16:17, 22 June 2022 diff hist 0 Pasting Lemma/Pair of Continuous Mappings on Open Sets
- 16:16, 22 June 2022 diff hist −432 Pasting Lemma/Pair of Continuous Mappings on Open Sets
- 16:10, 22 June 2022 diff hist +162 User:Leigh.Samphier/Templates/CommonHeader
- 15:56, 22 June 2022 diff hist +31 User:Leigh.Samphier/Topology
- 15:12, 22 June 2022 diff hist −112 Finite Product of Weakly Locally Compact Spaces is Weakly Locally Compact