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• Notes:Quotient topology
  : '''Note to readers: ''' the page [[quotient topology]] as it stands right now ([[User:Alec|Alec]] ([[User talk:Alec|talk]]) 17:0 See [[Notes:Quotient topology plan]] for an outline of the page.
  6 KB (1,087 words) - 19:45, 26 April 2016
• Topological separation axioms
  ...ally provide a useful constraint on the topology. Consider for example the topology {{M|\mathcal{J} }} defined as: ...}} is some topology on {{M|[0,1]\subset\mathbb{R} }} (power-set / discrete topology being a good example)
  4 KB (569 words) - 00:08, 4 May 2016
• Types of topological retractions
  ==Definitions== {{Definition|Algebraic Topology|Homotopy Theory|Topology|Topological Manifolds|Manifolds}}
  482 B (50 words) - 04:26, 14 December 2016
• Notes:Types of retractions
  ==Definitions== ! Topology and Geometry
  6 KB (1,008 words) - 11:56, 2 June 2016
• Notes:Connected space
  ...nnected. Here I attempt to document them, as research for the [[connected (topology)|connectedness]] page. ==Definitions==
  1 KB (188 words) - 21:33, 30 September 2016
• Notes:Basis for a topology
  There's "basis for a topology" and "basis that generates a topology", the two are very similar constructs, and it is important to be able to mo ==Definitions==
  5 KB (966 words) - 16:56, 27 June 2016
• Notes:Generalising the limit
  I can parrot you back a few definitions for limit. These all have something similar though, it's just hard to phras ...nd {{M|V}} then it captures {{M|U\cap V}} - '''PROVED''' - remember that a topology is closed under finite intersection so this is applicable.
  6 KB (1,118 words) - 11:34, 30 July 2016
• Neighbourhoods
  {{Definition|Topology|Metric Space}}[[Category:Examples of conflicting definitions]]
  112 B (11 words) - 22:02, 4 August 2016
• Notes:Basis for a topology/Attempt 2
  Last time I tried to merge the definitions, which got very confusing! This time I shall treat them as separate things ==Definitions==
  9 KB (1,719 words) - 10:14, 8 August 2016
• Notes:Basis for a topology/New terminology
  ==Definitions== ...enerated topology (by a basis) and '''TBasis''' for a basis of an existing topology.
  2 KB (451 words) - 10:57, 8 August 2016
• A subset of a topological space is open if and only if it is a neighbourhood to all of its points
  :: {{Note|This proof is slightly more involved if you use the metric space definitions (rather than considering the metric space as a topological space)}} *** As {{M|\mathcal{J} }} is a [[topology]] we know it is closed under arbitrary [[union]] (the union of absolutely a
  8 KB (1,529 words) - 00:27, 6 September 2016
• Editing guide/Templates/Page categorisation
  | To categorise definitions ...categorise the page in the subject categories, the [[:Category:Definitions|definitions]] category and in the individual subject categories.
  653 B (80 words) - 10:11, 8 September 2016
• Notes:Quotient topology/Table
  ==Table of definitions== ! Quotient topology
  2 KB (327 words) - 16:09, 13 September 2016
• Topology generated by a basis/Statement
  ...space]] with {{M|\mathcal{B} }} being a {{link|basis|topology}} for the [[topology]] {{M|1=\{\bigcup\mathcal{A}\ \vert\ \mathcal{A}\in\mathcal{P}(\mathcal{B}) ...l{P}(X)]}} which is the same as (by [[power-set]] and [[subset of|subset]] definitions) {{M|\forall B\in\mathcal{B}[B\subseteq X]}}.
  3 KB (545 words) - 21:59, 15 January 2017
• Doctrine:Homotopy terminology
  Before we can define terms, here are the definitions we work with: {{Doctrine Of|Topology|Homotopy Theory}}
  3 KB (535 words) - 09:01, 31 October 2016
• Closed map
  : '''Note: ''' we really have an {{iff}} relationship here. See [[definitions and iff]] for information {{Definition|Topology}}
  1 KB (246 words) - 19:59, 26 September 2016
• Every surjective map gives rise to an equivalence relation
  ...Something in Topological Manifolds (Lee) should cover this. Under Quotient topology}} ...2\in X[x_1\sim x_2\iff f(x_1)=f(x_2)]}} (for the "and only if" part, see [[definitions and iff]])
  2 KB (315 words) - 13:54, 8 October 2016
• Dense
  ...definitions to here, as they're like... "easy equivalent" and may well be definitions, not like ... a proposition of equivalence. ...p="Note">These are not just logically equivalent to density, they could be definitions for density, and may well be in some books.</ref>
  6 KB (1,097 words) - 04:15, 1 January 2017
• Exercises:Mond - Topology - 1/Question 6
  ...hat it sends {{M|-1}} and {{M|1}} to the same point in {{M|\mathbb{S}^1}}. Definitions may be explicit or use a picture {{float-right|{{Exercises:Mond - Topology - 1/Pictures/Q6P1 - 1}}}}We shall define {{M|f:[-1,1]\rightarrow\mathbb{S}^
  7 KB (1,326 words) - 12:26, 12 October 2016
• Exercises:Mond - Topology - 1/Question 7
  {{float-right|{{Exercises:Mond - Topology - 1/Pictures/Q7 - 1}}}} Definitions:
  9 KB (1,732 words) - 23:26, 11 October 2016