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• Given two open balls sharing the same centre but with differing radius then the one defined to have a strictly smaller radius is contained in the other
  ...seteq B_{r_2}(x)}} (where {{M|B_\epsilon(x)}} denotes the [[open ball]] of radius {{M|\epsilon>0}} centred at {{M|x\in X}})
  2 KB (391 words) - 20:27, 16 January 2017
• Given two open balls sharing the same centre the one defined to have a strictly smaller radius is contained in the other
  ...but with differing radius then the one defined to have a strictly smaller radius is contained in the other]]
  165 B (28 words) - 20:27, 16 January 2017

Page text matches

• Open set
  ...(X)\subseteq U]}} - (recall that {{M|B_r(x)}} denotes the [[open ball]] of radius {{M|r}} centred at {{M|x}}) or ...ath>B_r(x)</math> the [[Open ball|open ball]] centred at <math>x</math> of radius <math>r</math>
  4 KB (677 words) - 02:26, 29 November 2015
• Open ball
  ...[[metric space]] {{M|(X,d)}} the ''open ball centred at {{M|x_0\in X}} of radius {{M|r>0}}'', denoted {{M|B_r(x_0)}} (however many notations are used, see b Here the notations denote an open ball of radius {{M|r}} centred at {{M|x}} (in a [[metric space]] {{M|(X,d)}}, this table i
  4 KB (842 words) - 02:00, 29 November 2015
• Continuity definitions are equivalent
  ...</math> in the ball, the thing <math>f</math> maps it to is in the ball of radius <math>\epsilon</math> about <math>f(x)</math>).
  2 KB (476 words) - 07:20, 27 April 2015
• Motivation for tangent space
  ...g|thumb|Some lines in polar coordinates, the y axis is the angle and the x radius<br/>all these lines have gradient 1 (the gradient would just affect where r
  6 KB (975 words) - 00:18, 11 April 2015
• Trivial topology
  ...such a metric existed it would have to have the [[Open ball|open ball]] of radius {{M|0}} as the entire of {{M|X}}, then no ''strict'' :subset of {{M|X}} (ex
  1 KB (235 words) - 16:41, 14 August 2015
• Notes:Spherical coordinates
  For a circle of radius 1 the angles at {{M|45^\circ}} to the poles occur when the height is exactl ==Why not just use the angles (and radius)?==
  10 KB (1,899 words) - 18:48, 23 September 2015
• Totally bounded
  ...exists\{B_i\}_{i=1}^n\text{ of} }} [[open ball|open balls]]{{M|1=\text{ of radius }\epsilon[X\subseteq\cup_{i=1}^n B_i]}}, that is: ...ll\epsilon>0}} there exists a finite collection of [[open balls]], each of radius {{M|\epsilon}}, such that the family of balls [[cover]] {{M|X}}
  626 B (101 words) - 19:44, 27 May 2016
• Lebesgue number lemma
  ...silon_x}(x)\subseteq U]}} (where {{M|B_r(x)}} denotes the [[open ball]] of radius {{M|r}} centred at {{M|x}})
  2 KB (333 words) - 10:11, 10 May 2016
• Task:Continuity types
  #** This means there is an [[open ball]] of some radius {{M|r>0}} centred at {{M|f(x)}}, {{M|B_r(f(x))}} such that {{M|B_r(f(x))\su
  3 KB (668 words) - 22:38, 4 August 2016
• Notes:Tangent space
  # Take the unit sphere, and take the sphere of double the radius, using charts how can we distinguish these?
  5 KB (1,002 words) - 19:42, 15 August 2016
• Dense
  ...)\cap E\ne\emptyset]}} - where {{M|B_r(x)}} denotes the [[open ball]] of [[radius]] {{M|r}}, centred at {{M|x}}
  6 KB (1,097 words) - 04:15, 1 January 2017
• Exercises:Mond - Topology - 1/Question 6
  ...at the point {{M|(1,0)}} and goes anticlockwise around the circle of unit radius once.
  7 KB (1,326 words) - 12:26, 12 October 2016
• Exercises:Mond - Topology - 1/Question 7
  ...} is the composition of maps in my diagram that take {{M|D^2}}, double its radius, then embed it in {{M|\mathbb{R}^3}} then "pop it out" into a hemisphere. W
  9 KB (1,732 words) - 23:26, 11 October 2016
• Exercises:Mond - Topology - 1/Pictures/Q7 - 1
  [[File:MondTop1Q7Map.JPG|thumb|The idea is to double the radius of {{M|D^2}}, then pop it out into a hemisphere, then pull the rim to a poi
  313 B (56 words) - 12:31, 8 October 2016
• Exercises:Mond - Topology - 1/Question 9
  Then just place one of these [[open balls]] of radius {{M|\epsilon}} at each of the 4 points. Job done!
  8 KB (1,450 words) - 12:34, 12 October 2016
• Exercises:Mond - Topology - 2/Section B/Question 5
  ...epsilon(v_3)\cap I^2}}, where the [[open ball]] {{M|1=B_\epsilon(v_3)}} of radius {{M|\epsilon}} centred at {{M|1=v_3}} is considered in {{M|\mathbb{R}^2}}, ...v_3;\mathbb{R}^2)\cap I^2}} - the [[intersection]] of the [[open ball]] of radius {{M|\epsilon}}, in {{M|\mathbb{R}^2}} and {{M|I^2}}, by definition of the [
  8 KB (1,427 words) - 08:30, 18 October 2016
• N-cell
  ...mathbb{B}^n} }} or {{M|\overline{\mathbb{B} }^n}}, is a [[closed ball]] of radius {{M|1}} based at the origin. ...">The open unit ball, denoted: {{M|\mathbb{B}^n }}, is an [[open ball]] of radius {{M|1}} based at the origin.
  2 KB (369 words) - 19:57, 14 January 2017
• If the intersection of two open balls is non-empty then for every point in the intersection there is an open ball containing it in the intersection
  ...n balls sharing the same centre the one defined to have a strictly smaller radius is contained in the other]] ...at overlap} }\underbrace{\exists r_3\in\mathbb{R}_{>0} }_{\text{there is a radius for the ball at }x_3}\overbrace{[x_3\in \ball{3}\wedge\underbrace{\ball{3}\
  6 KB (1,007 words) - 20:16, 16 January 2017
• Given two open balls sharing the same centre the one defined to have a strictly smaller radius is contained in the other
  ...but with differing radius then the one defined to have a strictly smaller radius is contained in the other]]
  165 B (28 words) - 20:27, 16 January 2017
• Topology induced by a metric
  ...<\epsilon}} so {{M|p\in B_\epsilon(p)}}</ref> denotes the [[open ball]] of radius {{M|\epsilon\in\mathbb{R}_{>0} }} centred at {{M|p\in X}}
  2 KB (388 words) - 12:05, 17 January 2017