User contributions for GrzegorzBancerek

5 September 2017

• 18:2018:20, 5 September 2017 diff hist +2,307‎ Mapping is Continuous implies Mapping Preserves Filtered Infima in Lower Topological Lattice ‎No edit summary

4 September 2017

• 17:1417:14, 4 September 2017 diff hist +1,827‎ N Mapping is Continuous implies Mapping Preserves Filtered Infima in Lower Topological Lattice ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ and $Q = \left({X, \preceq', \tau'}\right)$ be complete Definition:Topological Latti..."
• 15:0315:03, 4 September 2017 diff hist +1,082‎ If Infimum of Filtered Subset belongs to Element of Sub-Basis then Subset and Element Intersect implies Infimum of Subset belongs to Closure of Subset ‎No edit summary

2 September 2017

• 13:2913:29, 2 September 2017 diff hist 0‎ m If Infimum of Filtered Subset belongs to Element of Sub-Basis then Subset and Element Intersect implies Infimum of Subset belongs to Closure of Subset ‎No edit summary
• 13:2213:22, 2 September 2017 diff hist +921‎ If Infimum of Filtered Subset belongs to Element of Sub-Basis then Subset and Element Intersect implies Infimum of Subset belongs to Closure of Subset ‎No edit summary

1 September 2017

• 14:3414:34, 1 September 2017 diff hist +677‎ N If Infimum of Filtered Subset belongs to Element of Sub-Basis then Subset and Element Intersect implies Infimum of Subset belongs to Closure of Subset ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a complete topological lattice with Definition..."

31 August 2017

• 16:2416:24, 31 August 2017 diff hist +963‎ N Mapping Preserves Infima implies Mapping is Continuous in Lower Topological Lattice ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ and $Q = \left({X, \preceq', \tau'}\right)$ be complete Definition:Topological Latti..."

30 August 2017

• 18:1018:10, 30 August 2017 diff hist +497‎ Mapping Preserves Non-Empty Infima implies Mapping is Continuous in Lower Topological Lattice ‎No edit summary
• 17:4717:47, 30 August 2017 diff hist +1,532‎ Mapping Preserves Non-Empty Infima implies Mapping is Continuous in Lower Topological Lattice ‎No edit summary

29 August 2017

• 13:1613:16, 29 August 2017 diff hist +1,621‎ Mapping Preserves Non-Empty Infima implies Mapping is Continuous in Lower Topological Lattice ‎No edit summary

28 August 2017

• 15:0715:07, 28 August 2017 diff hist +1,599‎ N Mapping Preserves Non-Empty Infima implies Mapping is Continuous in Lower Topological Lattice ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ and $Q = \left({X, \preceq', \tau'}\right)$ be complete Definition:Topological Latti..."

27 August 2017

• 16:4516:45, 27 August 2017 diff hist +872‎ N Closed Subset is Upper Section in Lower Topology ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a transitive Definition:Relational Structure with Topology|relational structur..."
• 16:0616:06, 27 August 2017 diff hist +1,621‎ Open Subset is Lower Section in Lower Topology ‎No edit summary

26 August 2017

• 18:0818:08, 26 August 2017 diff hist +202‎ Open Subset is Lower Section in Lower Topology ‎No edit summary
• 17:2417:24, 26 August 2017 diff hist −94‎ m Definition:Relational Structure with Topology ‎No edit summary current
• 16:4016:40, 26 August 2017 diff hist −36‎ m Lower Topology is Unique ‎No edit summary
• 16:3916:39, 26 August 2017 diff hist 0‎ m Lower Topology is Unique ‎ GrzegorzBancerek moved page Two Lower Topologies are Equal to Lower Topology is Unique without leaving a redirect

25 August 2017

• 18:5318:53, 25 August 2017 diff hist +490‎ N Open Subset is Lower Section in Lower Topology ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a transitive Definition:Relational Structure with Topology|relational structur..."
• 18:0818:08, 25 August 2017 diff hist 0‎ m Complement of Upper Closure of Element is Open in Lower Topology ‎No edit summary
• 18:0618:06, 25 August 2017 diff hist +121‎ m Complement of Upper Closure of Element is Open in Lower Topology ‎No edit summary
• 17:0417:04, 25 August 2017 diff hist +917‎ N Complement of Upper Closure of Element is Open in Lower Topology ‎ Created page with "== Theorem == Let $T = \left({S, \preceq, \tau}\right)$ be a relational structure with Definition:Lower Topology|lower top..."

23 August 2017

• 14:3714:37, 23 August 2017 diff hist +906‎ N Lower Topology is Unique ‎ Created page with "== Theorem == Let $T_1 = \left({S, \preceq, \tau_1}\right)$ and $T_2 = \left({S, \preceq, \tau_2}\right)$ be Definition:Relational Structure with Topology|relational struct..."

22 August 2017

• 14:4914:49, 22 August 2017 diff hist +1,332‎ N Relational Structure admits Lower Topology ‎ Created page with "== Theorem == Let $R = \left({S, \preceq}\right)$ be a relational structure. Then there exists a Definition:Relational Structure with..."

21 August 2017

• 18:5718:57, 21 August 2017 diff hist +723‎ N Definition:Lower Topology ‎ Created page with "== Definition == Let $T = \left({S, \preceq, \tau}\right)$ be a relational structure with topology. Then $T$ has '''lower..." current

20 August 2017

• 15:0315:03, 20 August 2017 diff hist +549‎ N Definition:Weak Retract (Topology) ‎ Created page with "== Definition == Let $T_1 = \left({S_1, \tau_1}\right)$ and $T_2 = \left({S_2, \tau_2}\right)$ be topological spaces. Then $T_1$ is '''a we..."
• 14:1414:14, 20 August 2017 diff hist +655‎ N Definition:Image of Topological Space ‎ Created page with "== Definition == Let $T = \left({S, \tau}\right)$ and $Q = \left({X, \tau'}\right)$ be topological spaces. Let $f:S \to X$ be a Definition..."

19 August 2017

• 13:2213:22, 19 August 2017 diff hist 0‎ m Restriction of Composition is Composition of Restriction ‎No edit summary
• 13:1313:13, 19 August 2017 diff hist +1,410‎ N Restriction of Composition is Composition of Restriction ‎ Created page with "== Theorem == Let $X, Y, Z$ be sets. Let $f: X \to Y$ and $g: Y \to Z$ be Definition:Mapping:mappings. Let $S \subseteq X$. Then $\left({g \circ f}..."

18 August 2017

• 15:0115:01, 18 August 2017 diff hist +1,147‎ Retract of Injective Space is Injective ‎No edit summary

17 August 2017

• 16:1816:18, 17 August 2017 diff hist +1,272‎ Retract of Injective Space is Injective ‎No edit summary
• 12:5612:56, 17 August 2017 diff hist +48‎ m Definition:Retract (Topology) ‎No edit summary
• 12:4912:49, 17 August 2017 diff hist +53‎ m Definition:Retraction (Topology) ‎No edit summary
• 12:4112:41, 17 August 2017 diff hist +36‎ m Definition:Retraction (Topology) ‎No edit summary

15 August 2017

• 18:3018:30, 15 August 2017 diff hist +377‎ N Retract of Injective Space is Injective ‎ Created page with "== Theorem == Let $T = \left({S, \tau}\right)$ be an injective topological space. Let $R = \left({X, \tau'}\right)$ be a Definition:Retract..."
• 15:2015:20, 15 August 2017 diff hist +488‎ N Definition:Retract (Topology) ‎ Created page with "== Definition == Let $T_1 = \left({S_1, \tau_1}\right)$ be a topological space. Let $T_2 = \left({S_2, \tau_2}\right)$ be a Definition:Top..."
• 15:0515:05, 15 August 2017 diff hist +498‎ N Definition:Retraction (Topology) ‎ Created page with "== Definition == Let $T_1 = \left({S_1, \tau_1}\right)$ be a topological space. Let $T_2 = \left({S_2, \tau_2}\right)$ be a Definition:Top..."
• 13:5713:57, 15 August 2017 diff hist +517‎ N Product of Injective Spaces is Injective ‎ Created page with "== Theorem == Let $I$ be a non-empty set. Let $\left({\left({S_i, \tau_i}\right)}\right)_{i \in I}$ be an Definition:Indexe..."

9 August 2017

• 15:4015:40, 9 August 2017 diff hist +959‎ N Definition:Injective Space ‎ Created page with "== Definition == Let $Z = \left({S, \tau_1}\right)$ be a topological space. Then $Z$ is '''injective (space)''' {{iff}} :for all Definitio..." current

5 August 2017

• 17:1117:11, 5 August 2017 diff hist +3,424‎ N Continuous iff Mapping at Element is Supremum of Compact Elements ‎ Created page with "== Theorem == Let $L = \left({S, \preceq_1, \tau_1}\right)$ and $R = \left({T, \preceq_2, \tau_2}\right)$ be complete Definition:Algebraic O..."

4 August 2017

• 12:5012:50, 4 August 2017 diff hist +1,867‎ N Continuous iff Mapping at Element is Supremum ‎ Created page with "== Theorem == Let $\left({S, \preceq_1, \tau_1}\right)$ and $\left({T, \preceq_2, \tau_2}\right)$ be complete Definition:Continuous Ordered..." current

3 August 2017

• 13:4813:48, 3 August 2017 diff hist +2,535‎ N Mapping at Element is Supremum of Compact Elements implies Mapping at Element is Supremum that Way Below ‎ Created page with "== Theorem == Let $\left({S, \vee_1, \wedge_1, \preceq_1}\right)$ and $\left({T, \vee_2, \wedge_2, \preceq_2}\right)$ be complete lattices. L..."

2 August 2017

• 19:1219:12, 2 August 2017 diff hist +1,917‎ N Mapping at Element is Supremum of Compact Elements implies Mapping is Increasing ‎ Created page with "== Theorem == Let $\left({S, \vee_1, \wedge_1, \preceq_1}\right)$ be a lattice. Let $\left({T, \vee_2, \wedge_2, \preceq_2}\right)$ be a Definition:..."
• 13:5113:51, 2 August 2017 diff hist +9‎ m Open Set is Union of Elements of Basis ‎No edit summary
• 13:5013:50, 2 August 2017 diff hist +9‎ m Interior is Union of Elements of Basis ‎No edit summary current
• 13:3313:33, 2 August 2017 diff hist +1,291‎ N Open Set is Union of Elements of Basis ‎ Created page with "== Theorem == Let $T = \left({S, \tau}\right)$ be a topological space. Let $B$ be a basis of $T$. Let $V$ be..."

1 August 2017

• 18:5418:54, 1 August 2017 diff hist +338‎ Interior is Union of Elements of Basis ‎No edit summary
• 18:3818:38, 1 August 2017 diff hist +483‎ N Interior is Union of Elements of Basis ‎ Created page with "== Theorem == Let $T = \left({S, \tau}\right)$ be a topological space. Let $B$ be a basis of $T$. Let $V$ be..."
• 13:2213:22, 1 August 2017 diff hist +1,223‎ Characterization of Analytic Basis by Local Bases ‎No edit summary

31 July 2017

• 17:2917:29, 31 July 2017 diff hist +379‎ N Characterization of Analytic Basis by Local Bases ‎ Created page with "== Theorem == Let $T = \left({S, \tau}\right)$ be a topological space. Let $P$ be a set of Definition:Subset|su..."
• 16:4216:42, 31 July 2017 diff hist +1,700‎ N Way Above Closures that Way Below Form Local Basis ‎ Created page with "== Theorem == Let $L = \left({S, \preceq, \tau}\right)$ be a complete continuous Definition:Topologica..."