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    2 KB (268 words) - 13:37, 20 April 2016
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  • {| class="wikitable" border="1" * An [[equivalence class]] is the name given to the set of all things which are equivalent under a g
    3 KB (522 words) - 15:18, 12 February 2019
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  • An class {{M|R}} of sets is an ''Algebra of sets'' if<ref>p21 - Halmos - Measure The
    3 KB (507 words) - 18:43, 1 April 2016
  • A non-empty class of sets {{M|S}} is a {{sigma|ring}} if<ref>Measure Theory, p24 - Halmos - G
    728 B (125 words) - 15:34, 13 March 2015
  • : See [[Class of sets closed under set-subtraction properties|Properties of a class of sets closed under set subtraction]] * [[Class of sets closed under set-subtraction properties|Properties of a class of sets closed under set subtraction]]
    8 KB (1,306 words) - 01:49, 19 March 2016
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  • ...on is simply a [[Function|function]] with a domain of definition that is a class of sets<ref>Halmos - Measure Theory - p30 - Springer - Graduate Texts in Ma
    355 B (54 words) - 16:10, 13 March 2015
  • ...ra Maths}}A ''[[real valued function|real valued]]'' [[set function]] on a class of [[set|sets]], {{M|\mathcal{A} }}, {{M|f:\mathcal{A}\rightarrow\mathbb{R}
    6 KB (971 words) - 18:16, 20 March 2016
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    6 KB (941 words) - 14:39, 16 August 2016
  • Given any class of sets {{M|A}}, there exists a unique ring {{M|R_0}} such that {{M|E\subse If {{M|A}} is any class of sets, then every set in {{M|R(A)}} can be covered by a finite union of s
    2 KB (307 words) - 07:24, 27 April 2015
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    6 KB (1,190 words) - 19:27, 14 April 2015
  • Germs are an [[Equivalence class]] of an [[Equivalence relation]], rather than the usual way of denoting equ A germ is an [[Equivalence class|equivalence class]] of an [[Equivalence relation|equivalence relation]] defined as follows:
    2 KB (285 words) - 01:36, 5 April 2015
  • Given an [[Equivalence relation]] {{M|\sim}} the equivalence class of {{M|a}} is denoted as follows: An equivalence class may be denoted by {{M|[a]}} where {{M|a}} is the ''representative'' of it.
    1 KB (160 words) - 20:00, 14 November 2015
  • We could define a smooth structure as an [[Equivalence class]] of smooth atlases however it is far easier to use the second option
    2 KB (246 words) - 07:10, 7 April 2015
  • {| class="wikitable" border="1" ...s {{M|p:(x,y)\mapsto[(x,y)]}} where {{M|[(x,y)]}} denotes an [[Equivalence class]] - as usual.
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    6 KB (975 words) - 00:18, 11 April 2015
  • * <math>\pi_1(X,x_0)</math> denotes the set of [[Homotopy class|homotopy classes]] of [[Paths and loops in a topological space|loops]] base See [[Homotopy class]] for these properties
    3 KB (393 words) - 16:10, 4 November 2016
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    403 B (61 words) - 18:10, 16 April 2015
  • Using a bit of abstract algebra it is not hard to see that the [[Equivalence class|equivalence classes]] are exactly the [[Coset|cosets]] of {{M|\mathbb{Z} }} ...en {{M|a,b\in [t]}} we know {{M|a\sim b}} as {{M|[t]}} is an [[Equivalence class]]
    3 KB (592 words) - 16:57, 11 May 2015
  • The [[Equivalence class|equivalence class]] of {{M|\alpha}} is denoted (as is usual) by {{M|[\alpha]}}
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  • {| class="wikitable" border="1" ! Class
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