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- 16:54, 21 February 2018 Open Ordinal Space is not Compact in Closed Ordinal Space (hist) [1,182 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Gamma$ be a limit ordinal. Let $\left[{0 \,.\,.\, \Gamma}\right]$ denote the Definition:Closed Ordinal Space|closed ordina...")
- 17:12, 20 February 2018 Ordinal Space is Locally Compact (hist) [639 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T$ denote an ordinal space on a limit ordinal $\Gamma$. Then $T$ is a Definition:Locally Comp...")
- 16:56, 20 February 2018 Closed Ordinal Space is Compact (hist) [811 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Gamma$ be a limit ordinal. Let $\left[{0 \,.\,.\, \Gamma}\right]$ denote the Definition:Closed Ordinal Space|closed ordina...")
- 02:26, 19 February 2018 Closed Ordinal Space is Complete Order Space (hist) [1,057 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Gamma$ be a limit ordinal. Let $\left[{0 \,.\,.\, \Gamma}\right]$ denote the Definition:Closed Ordinal Space|closed ordina...")
- 17:45, 18 February 2018 Countable Open Ordinal Space is Metrizable (hist) [1,396 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\Gamma$ be a limit ordinal which Defi...")
- 17:33, 18 February 2018 Countable Closed Ordinal Space is Metrizable (hist) [1,404 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\Gamma$ be a limit ordinal which Defi...")
- 17:08, 18 February 2018 Minimal Polynomial of Element with Finite Orbit under Group of Automorphisms over Fixed Field in terms of Orbit (hist) [2,823 bytes] Barto (talk | contribs) (Created page with "== Theorem == Let $E$ be a field. Let $G \leq \operatorname{Aut}(E)$ be a subgroup of its Definition:Automorphism Group of Fie...")
- 17:07, 18 February 2018 Countable Open Ordinal Space is Second-Countable (hist) [1,799 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\Gamma$ be a limit ordinal which Defi...")
- 17:05, 18 February 2018 Countable Closed Ordinal Space is Second-Countable (hist) [1,811 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\Gamma$ be a limit ordinal which Defi...")
- 17:02, 18 February 2018 Finite Orbit under Group of Automorphisms of Field implies Separable over Fixed Field (hist) [1,150 bytes] Barto (talk | contribs) (Created page with "== Theorem == Let $E$ be a field. Let $G \leq \operatorname{Aut}(E)$ be a subgroup of its Definition:Automorphism Group of Fie...")
- 16:12, 18 February 2018 Subextensions of Separable Field Extension are Separable (hist) [1,098 bytes] Barto (talk | contribs) (Created page with "== Theorem == Let $E/K/F$ be a tower of fields. Let $E/F$ be separable. Then $E/K$ and $K/F$ are ...")
- 15:21, 18 February 2018 Separable Elements Form Field (hist) [440 bytes] Barto (talk | contribs) (Created page with "== Theorem == Let $E/F$ be an algebraic field extension. Then the subset of Definition:Separable Element of...")
- 11:55, 18 February 2018 Ring Element is Invertible iff Invertible in Integral Extension (hist) [896 bytes] Barto (talk | contribs) (Created page with "== Theorem == let $A$ be a commutative ring with unity. Let $a \in A$. Let $B$ be an Definition:Integral Ring Extension|integra...")
- 10:07, 18 February 2018 Uncountable Open Ordinal Space is not Second-Countable (hist) [747 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right)$ denote the Definition:Uncountabl...")
- 10:06, 18 February 2018 Uncountable Closed Ordinal Space is not Second-Countable (hist) [755 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 07:39, 18 February 2018 Uncountable Closed Ordinal Space is not Perfectly Normal (hist) [1,500 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 06:04, 18 February 2018 Ordinal Space is Completely Normal (hist) [1,062 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Gamma$ denote a limit ordinal. Let $\left[{0 \,.\,.\, \Gamma}\right)$ denote the Definition:Open Ordinal Space|open ordina...")
- 06:00, 18 February 2018 Uncountable Open Ordinal Space is First-Countable (hist) [930 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right)$ denote the Definition:Uncountabl...")
- 05:46, 18 February 2018 Uncountable Closed Ordinal Space is not Separable (hist) [1,504 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 05:41, 18 February 2018 Uncountable Open Ordinal Space is not Separable (hist) [2,305 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right)$ denote the Definition:Uncountabl...")
- 05:17, 18 February 2018 Omega as Limit Point of Intervals of Uncountable Closed Ordinal Space (hist) [866 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 03:34, 17 February 2018 Uncountable Closed Ordinal Space is not First-Countable (hist) [1,236 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 18:14, 16 February 2018 Omega is Closed in Uncountable Closed Ordinal Space but not G-Delta Set (hist) [2,145 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Omega$ denote the first uncountable ordinal. Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the Definition:Uncountabl...")
- 13:28, 16 February 2018 Basis for Open Ordinal Topology (hist) [1,091 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\Gamma$ be a limit ordinal. Let $\left[{0 \,.\,.\, \Gamma}\right)$ denote the Definition:Open Ordinal Space|open ordinal sp...")
- 02:32, 16 February 2018 Every Point except Endpoint in Connected Linearly Ordered Space is Cut Point (hist) [1,101 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Let $A \subseteq S$ be a Definition:Connected To...")
- 09:43, 15 February 2018 Norm of Self-Adjoint Operator/Corollary (hist) [683 bytes] Prime.mover (talk | contribs) (Created page with "== Corollary to Norm of Self-Adjoint Operator == Let $H$ be a Hilbert space. Let $A \in B \left({H}\right)$ be a Definition:Self-Adjoint O...")
- 03:23, 14 February 2018 Linearly Ordered Space is Compact iff Complete (hist) [2,791 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Then $T$ is a Definition:Compact Topological Spa...")
- 01:48, 14 February 2018 Linearly Ordered Space is Completely Normal (hist) [895 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Then $T$ is a Definition:Completely Normal Space...")
- 01:43, 14 February 2018 Linearly Ordered Space is T1 (hist) [1,558 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Then $T$ is a Definition:Fréchet Space (Topolog...")
- 18:25, 13 February 2018 Linearly Ordered Space is T5 (hist) [4,723 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Then $T$ is a $T_5$ space....")
- 17:07, 13 February 2018 Successor Sets of Linearly Ordered Set Induced by Convex Component Partition (hist) [2,934 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Let $A$ and $B$ be Definition:Separated Sets|sep...")
- 15:58, 13 February 2018 Partition of Linearly Ordered Space by Convex Components is Linearly Ordered Set (hist) [1,718 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Let $A$ and $B$ be Definition:Separated Sets|sep...")
- 14:37, 13 February 2018 Generators of the special linear group of order 2 over the integers (hist) [2,331 bytes] Afropug (talk | contribs) (This gives a standard set of generators for SL$_2(\Z)$.)
- 08:00, 13 February 2018 Riesz Representation Theorem (Hilbert Spaces)/Corollary (hist) [876 bytes] Prime.mover (talk | contribs) (Created page with "== Corollary to Riesz Representation Theorem (Hilbert Spaces) == Let $H$ be a Hilbert space. Let $L$ be a Definition:Bounded Linear Functi...")
- 01:49, 13 February 2018 Separated Subsets of Linearly Ordered Space under Order Topology/Lemma (hist) [2,298 bytes] Prime.mover (talk | contribs) (Created page with "== Lemma == Let $T = \left({S, \preceq, \tau}\right)$ be a linearly ordered space. Let $A$ and $B$ be Definition:Separated Sets|separ...") originally created as "Separated Subsets of Linearly Ordered Set under Order Topology/Lemma"
- 03:09, 12 February 2018 Heine-Borel Theorem/Euclidean Space/Necessary Condition (hist) [763 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> For any natural number $n \ge 1$, a closed and Definition:Bounded Metric Spac...")
- 01:39, 12 February 2018 Subset of Convex Set can be Uniquely Expressed as Partition of Maximal Convex Sets (hist) [651 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\left({S, \preccurlyeq}\right)$ be an ordered set. Then $S$ can be uniquely expressed as the Definition...")
- 10:25, 11 February 2018 Union of Non-Disjoint Convex Sets is Convex Set (hist) [1,978 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\left({S, \preccurlyeq}\right)$ be an ordered set. Let $\mathcal C$ be a set of Definition:Convex...")
- 07:10, 11 February 2018 Convex Set of Ordered Set is not necessarily Interval (hist) [888 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\left({S, \preccurlyeq}\right)$ be an ordered set. Let $C$ be a convex set of $S$. T...")
- 06:37, 11 February 2018 Interval of Totally Ordered Set is Convex (hist) [2,710 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\left({S, \preccurlyeq}\right)$ be an ordered set. Let $I \subseteq S$ be an interval in...")
- 04:52, 11 February 2018 Equivalence of Definitions of Convex Set (Order Theory) (hist) [1,812 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{TFAE|def = Convex Set (Order Theory)|view = Convex Set|context = Order Theory}} === Definition 1 === {{...")
- 04:16, 11 February 2018 Equivalence of Definitions of Order Topology (hist) [1,689 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{TFAE|def = Order Topology}} === Definition 1 === {{:Definition:Order Topology/Definition 1}} === Definition:Orde...")
- 19:34, 10 February 2018 Hilbert Cube is Arc-Connected (hist) [1,515 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is an arc-connected space....")
- 19:15, 10 February 2018 Hilbert Cube is Compact (hist) [1,504 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is a compact space....")
- 18:47, 10 February 2018 Hilbert Cube is Second-Countable (hist) [695 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is a Definition:Second-Countable Space|second-countable spa...")
- 18:45, 10 February 2018 Hilbert Cube is Separable (hist) [1,057 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is a separable space. == Pro...")
- 18:41, 10 February 2018 Hilbert Cube is Completely Normal (hist) [587 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is a Definition:Completely Normal Space|completely normal s...")
- 16:53, 10 February 2018 Hilbert Cube is Homeomorphic to Countable Infinite Product of Real Number Unit Intervals (hist) [1,576 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M_1 = \left({I^\omega, d_2}\right)$ be the Hilbert cube: :$M_1 = \displaystyle \prod_{k \mathop \in \N} \left[{0 \,.\,.\, \dfr...")
- 16:11, 10 February 2018 Hilbert Cube is Metric Space (hist) [787 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $M = \left({I^\omega, d_2}\right)$ be the Hilbert cube. Then $M$ is a metric space. <...")
- 10:21, 10 February 2018 Separable Metric Space is Homeomorphic to Subspace of Fréchet Metric Space (hist) [1,312 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $M = \left({A, d}\right)$ be a metric space whose induced topology is Definition:Sep...")