# User contributions

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- 16:03, 12 August 2009
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**+921** N Definition talk:Riemann Surface Created page with '== Changes == The previous definition wasn't quite correct - the point is that the transition maps should be holomorphic, and you cannot expect every open set (not even every op…' - 16:00, 12 August 2009
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**+2,192** Definition:Riemann Surface Definition wasn't quite correct; changed it to the standard one, added more details and properties. See Talk Page. - 02:12, 12 August 2009
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**+2,771** N Extremal Length of Composition Added this statement, which promises to be useful for further proofs. Provided a fairly detailed proof. - 16:15, 8 March 2009 diff hist +472 Talk:Main Page →Open Hypotheses
- 16:11, 8 March 2009 diff hist +138 Talk:Main Page →Stubs, stubs and stubs
- 16:07, 8 March 2009 diff hist -9 m Series Law for Extremal Length
- 16:07, 8 March 2009 diff hist +117 m Comparison Principle for Extremal Length
- 16:07, 8 March 2009
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**+1,429** N Comparison Principle for Extremal Length New page: == Proposition == Let <math>X</math> be a Riemann surface. Let <math>\Gamma_1</math> and <math>\Gamma_2</math> be families of [[Definition:Rectifiable Curve... - 15:56, 8 March 2009
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**+1,795** N Parallel Law for Extremal Length New page: == Proposition == Let <math>X</math> be a Riemann surface. Let <math>\Gamma_1</math>, <math>\Gamma_2</math> be families of [[Definition:Rectifiable Curve|re... - 15:46, 8 March 2009
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**+2,798** N Extremal Length of Union New page: == Proposition == Let <math>X</math> be a Riemann surface. Let <math>\Gamma_1</math> and <math>\Gamma_2</math> be families of [[Definition:Rectifiable Curve... - 13:11, 8 March 2009 diff hist -12 Definition:Component (Topology) →Alternative Definitions
- 13:10, 8 March 2009 diff hist +28 Definition:Component (Topology) →Alternative Definitions
- 13:10, 8 March 2009 diff hist +68 Definition talk:Component (Topology)
- 12:06, 8 March 2009
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**+1,018** N Talk:Series Law for Extremal Length/Rho is Well Defined New page: I've added this page as "proof of concept" regarding the idea of using subpages. The point about having this as a subpage is that a) the claim is easy to believe, easy to check, and the ... - 12:00, 8 March 2009
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**+1,047** N Series Law for Extremal Length/Rho is Well Defined This is a bit clumsy, since we don't have the basic notations of differential geometry yet. - 11:46, 8 March 2009
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**+3,148** N Series Law for Extremal Length New page: == Proposition == Let <math>X</math> be a Riemann surface. Let <math>\Gamma_1</math>, <math>\Gamma_2</math> and <math>\Gamma</math> be families of [[Definit... - 11:29, 8 March 2009 diff hist +116 m Definition:Extremal Length Added reference to Ahlfors.
- 00:08, 8 March 2009
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**+1,821** User talk:Lasserempe - 21:01, 7 March 2009
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**+738** Talk:Union of Connected Sets with Non-Empty Intersections is Connected - 19:50, 7 March 2009 diff hist +194 Talk:Main Page →Open Hypotheses
- 19:09, 7 March 2009
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**+1,387** N User:Lasserempe New page: I am a research mathematician. It seems to me that ProofWiki is a worthwhile project for having mathematical proofs available online. I also see some concerns, namely that there will nee... current - 18:53, 7 March 2009
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**+4,018** N Properties of Grötzsch and Teichmüller Moduli Created proof. There are still some places where we are using basic facts about extremal length that should at some point be formalized. But this is probably all for me for today. - 18:31, 7 March 2009 diff hist +36 m Definition:Grötzsch Annulus
- 18:30, 7 March 2009 diff hist 0 m Definition:Teichmüller Annulus Definition:Teichmüller annulus moved to Definition:Teichmüller Annulus: Also forgot capitalization ...
- 18:30, 7 March 2009 diff hist +18 Definition:Teichmüller Annulus
- 18:30, 7 March 2009 diff hist +11 Definition:Teichmüller Annulus
- 18:29, 7 March 2009 diff hist 0 m Definition:Teichmüller Annulus Teichmüller annulus moved to Definition:Teichmüller annulus: Forgot to add "Definition" to page name when creating.
- 17:28, 7 March 2009 diff hist 0 m Definition:Grötzsch Annulus
- 16:51, 7 March 2009
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**+813** N Definition:Teichmüller Annulus New page: Let <math> R > 0 </math>. The set :<math>A := \C\setminus ([-1,0]\cup [R,\infty)) </math> is called a '''Teichmüller annulus''' (or also '''Teichmüller extremal domain'''). The ... - 16:48, 7 March 2009 diff hist -2 m Definition:Grötzsch Annulus →Properties
- 16:47, 7 March 2009
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**+725** N Definition:Grötzsch Annulus New page: Let <math> R > 0 </math>. The set :<math>A := \{z\in\C: |z|>1 \text{ and } z\notin [R,\infty) \}</math> is called a '''Grötzsch annulus''' (or also '''Grötzsch extremal domain'''). The ... - 16:32, 7 March 2009 diff hist +358 Definition:Totally Disconnected Space
- 15:59, 7 March 2009 diff hist +430 Equivalence of Definitions of Component
- 15:51, 7 March 2009 diff hist +3 Definition talk:Component (Topology)
- 15:51, 7 March 2009 diff hist +312 N Definition talk:Component (Topology) New page: The previous statement of the alternative definition was incorrect. Indeed, the empty set (viewed as a topological space) has no connected component, since every connected component is emp...
- 15:50, 7 March 2009 diff hist +419 Definition:Component (Topology) Corrected alternative definition and added another.
- 15:41, 7 March 2009 diff hist +145 Union of Connected Sets with Non-Empty Intersections is Connected Changed statement - I do not see the point of using 'index sets', even though many textbooks do; as a student I always found this unnecessarily complicated. (But am open for discussion.)
- 15:18, 7 March 2009 diff hist 0 m Union of Connected Sets with Non-Empty Intersections is Connected Union of Connected Intersections is Connected moved to Spaces with Connected Intersection have Connected Union: The previous title was ambiguous.
- 14:56, 7 March 2009
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**+997** N Definition:Golden Mean New page: The '''golden mean''' is the unique positive real number <math>\phi</math> satisfying :<math>\phi = \frac{1}{\phi-1}.</math> (A geometric interpretation of this condition is as follows: i... - 14:16, 7 March 2009 diff hist +1 m Definition:Complete Metric Space
- 13:46, 7 March 2009 diff hist +22 m Definition:Complete Metric Space
- 13:45, 7 March 2009
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**-3,909** Convergent Sequence is Cauchy Sequence Removed second part; included reference to completeness. Also cleaned up proof a little bit. - 13:23, 7 March 2009 diff hist 0 Definition:Complete Metric Space
- 13:23, 7 March 2009
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**+1,113** N Real Number Line is Complete Metric Space New page: == Theorem == The real numbers <math>\R</math>, equipped with the usual Euclidean metric, are a complete metric space. == Proof == See [[Real Number ... - 13:13, 7 March 2009
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**+996** N Definition:Complete Metric Space New page: A metric space <math>(X,d)</math> is called '''complete''' if every Cauchy sequence is convergent. == Examples == The s... - 12:15, 7 March 2009 diff hist +144 Talk:Convergent Sequence is Cauchy Sequence
- 12:13, 7 March 2009
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**+761** N Talk:Convergent Sequence is Cauchy Sequence New page: A space in which every Cauchy sequence is convergent is called complete. Hence we should simply remark here that a space where the converse holds is called complete, with a reference to th... - 11:43, 7 March 2009 diff hist +44 m Definition:Modulus →Geometric Function Theory
- 11:42, 7 March 2009
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**+1,942** N Invariance of Extremal Length under Conformal Mappings Created proof. It might have been easier just for plane domains, but seems nice to have a general statement. May need to add a few more details at some point. - 11:18, 7 March 2009 diff hist +1 m Definition:Extremal Length →Extensions of the concept