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• Homeomorphism
  ...{{M|f:X\rightarrow Y}} where both {{M|f}} and {{M|f^{-1} }} (the [[inverse function]]) are [[continuous]] * There exists a [[Function|mapping]] {{M|f:(X,d)\rightarrow(Y,d')}} such that:
  5 KB (731 words) - 22:58, 22 February 2017
• Surjection
  * Factor out composition theorem into own page. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 21:56, The composition of surjective functions is surjective
  2 KB (263 words) - 21:56, 8 May 2018
• Measurable map
  '''Note: ''' Sometimes called a ''measurable [[Function|fuction]]''<ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref> ...icely for composition. As [[Composition of measurable maps is measurable|a composition of measurable maps is measurable]]<ref name="PAS"/> we see something like,
  5 KB (792 words) - 02:31, 3 August 2015
• Smooth manifold
  ===Smooth function=== ...n a [[Smooth manifold|smooth {{n|manifold}}]], {{M|(M,\mathcal{A})}}, is a function<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> {{
  3 KB (413 words) - 21:09, 12 April 2015
• Smooth function
  ...n a [[Smooth manifold|smooth {{n|manifold}}]], {{M|(M,\mathcal{A})}}, is a function<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> {{ ...psi(U\cap V)\rightarrow\mathbb{R} }} which is [[Smooth|smooth]] as it is a composition of smooth functions
  3 KB (560 words) - 16:16, 14 April 2015
• Passing to the quotient (function)
  ...tyle=max-width:20em;}}Given a function, {{M|f:X\rightarrow Y}} and another function, {{M|w:X\rightarrow W}}<ref group="Note">I have chosen {{M|W}} to mean "wha ...P}(A)}} (a subset of {{M|A}}) we use {{M|f(D)}} to denote the {{link|image|function}} of {{M|D}} under {{M|f}}, namely: {{M|1=f(D):=\{f(d)\in B\ \vert\ d\in D\
  8 KB (1,644 words) - 20:49, 11 October 2016
• Partition (combinatorics)
  * [[Composition (combinatorics)]] * [[Monomial symmetric function]] - the motivation for these partitions
  2 KB (254 words) - 14:30, 17 June 2015
• Site projects:Patrolling measure theory/Task list
  * [[Additive function]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:50, 19 March 2 * [[Integral of a simple function (measure theory)]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]])
  5 KB (645 words) - 11:40, 21 August 2016
• Category
  # A function called ''composition of morphisms'':
  2 KB (347 words) - 00:36, 27 September 2015
• Notes:Quotient
  # The dashed arrow exists by function composition. # Using the [[Factor (function)]] idea, if we have (for {{M|(v,v')\in V\times V}} and {{M|(u,u')\in V\time
  3 KB (588 words) - 09:38, 24 November 2015
• Quotient vector space
  * The diagonal arrow labeled as {{M|\pi\circ+}} exists by composition of the: ...pi:V\times V\rightarrow\frac{V}{\sim}\times\frac{V}{\sim} }} is simply the function:
  5 KB (879 words) - 23:09, 1 December 2016
• Category Theory (subject)
  ...or spaces, like [[group|groups]] or [[topological space|topologies]] and [[function|functions]] between them, like [[homomorphism (group)|group homomorphisms]] ...ey should see [[Example of a category whose arrows compose not by function composition]].
  2 KB (311 words) - 11:46, 19 February 2016
• A continuous map induces a homomorphism between fundamental groups
  ...tant precursor theorem: [[The relation of path-homotopy is preserved under composition with continuous maps]]. ...es]], {{Top.|X|J}} and {{Top.|Y|K}} (which may be the same) a [[continuous function]], {{M|f:X\rightarrow Y}} induces a [[group homomorphism]] between the [[fu
  877 B (135 words) - 03:55, 14 December 2016
• Permutation of a set
  * A ''[[bijective]]'' [[function]], {{M|f:X\rightarrow X}}. Recall that bijective means [[injective]] (1:1) : [[The collection of all permutations of a set forms a group under function composition]] - see the [[permutation group]]. The [[symmetric group]] is a special cas
  870 B (134 words) - 23:59, 21 July 2016
• Notes:Generalising the limit
  ...preceq)}} and {{M|(Q,\le)}} - both satisfying the forward property - and a function {{M|\alpha:Q\rightarrow P}} if{{M|\alpha}} satisfies: ...'' this works but I have not completed my work. The obvious tests are that composition preserves "the forwardness property" and that it works for a [[sub-sequence
  6 KB (1,118 words) - 11:34, 30 July 2016
• Composition of functions
  #REDIRECT [[Function composition]]
  82 B (9 words) - 12:24, 15 September 2016
• Demonstrating why category arrows are best thought of as arrows and not functions
  ...k|arrow|category theory|s}}, {{M|\xymatrix{A \ar[r]^f & B} }} are {{plural|function|s}}{{rAITCTHS2010}}: ...rrow\mathbb{R} }}<ref name="AITCTHS2010"/><ref group="Note">Yes, this is a function, but wait and you'll see this is quite different to the "usual" kind of arr
  2 KB (275 words) - 12:29, 15 September 2016
• Exercises:Mond - Topology - 1/Question 7
  * {{M|E:D^2\rightarrow H}} is the composition of maps in my diagram that take {{M|D^2}}, double its radius, then embed it ...define {{M|f:D^2\rightarrow\mathbb{S}^2}} to be the [[function composition|composition]] of {{M|E}} and {{M|f'}}, that is: {{M|1=f:=f'\circ E}}, meaning {{M|f:x\m
  9 KB (1,732 words) - 23:26, 11 October 2016
• Notes:Modules
  ...rrow V}} is the identity map, and {{M|\tau^3}} is the threefold [[function composition]] {{M|\tau\circ\tau\circ\tau}}
  4 KB (808 words) - 17:18, 11 October 2016
• Concatenation of paths and loops (homotopy)
  ...e same basepoint"</ref> - then we define their [[concatenation]] ({{AKA}}: composition, product){{rITTMJML}} as follows: ** Note that {{M|1=t=\frac{1}{2} }} is in both parts of the [[piecewise function]], this is to emphasise that {{M|(f*g)(\frac{1}{2})}} is the same in either
  2 KB (351 words) - 00:57, 15 October 2016