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• Continuous map/Refactoring tasks
  # [[A map is continuous if and only if the pre-image of every closed set is closed]] ...d only if each point in the domain has an open neighbourhood for which the restriction of the map is continuous on]]
  249 B (46 words) - 01:46, 14 October 2016
• Exercises:Saul - Algebraic Topology - 1/Exercise 1.2
  ...f(y)\})}} is a map similar to the [[restriction]] of {{M|f}}, but with the image of the point removed, removed from the codomain also.</ref> - by removing a ...) we must conclude {{M|\sf{C} }} is none of the existing groups and founds its own.
  17 KB (3,132 words) - 12:03, 18 January 2017
• Notes:CW-Complex
  ...b{B}^m}\right)}}</ref> ''[[homeomorphism|homeomorphically]]'' [[surjection|onto]] {{M|e_\alpha}} and ...o-domain, it is a common first-year mistake to look at the association of "onto" with "surjection" and associate into with "injection" - I mention this her
  10 KB (1,736 words) - 01:00, 23 January 2017
• Local homeomorphism
  * {{M|f\vert_A^\text{Im}:A\rightarrow f(A)}} is the [[restriction onto its image]] of a [[function]]. ...{{M|f(U)}} is open in {{M|Y}} and {{M|f}} restricted to {{M|U}} (onto the image of {{M|U}}) is a [[homeomorphism]] (when {{M|U}} and {{M|f(U)}} are conside
  2 KB (271 words) - 21:45, 22 February 2017
• Evenly covered by a continuous map
  ...ha\in I}V_\alpha}} - the [[union]] of this family is the entire {{link|pre-image|function}} of {{M|U}}<ref group="Note">Note that both sides of the {{M|\eq} ...onto its image]] of {{M|f}} for each {{M|V_\alpha}} is a [[homeomorphism]] onto {{M|U}}
  2 KB (394 words) - 21:54, 24 February 2017
• Unique lifting property
  ...call that ''[[a set is open if and only if it is a neighbourhood to all of its points]]'', this is what we hope to show. ...ng map [[restricted to its image]] on {{M|V_\beta}} is a [[homeomorphism]] onto {{M|U}}
  13 KB (2,510 words) - 16:23, 2 March 2017
• Given a homeomorphism all subspaces of the domain are homeomorphic to their image under the homeomorphism itself/Statement
  ...{{M|f\vert_{A}^\text{Im}:A\rightarrow f(A)}} - the [[restriction onto its image]] of {{M|f}} to {{M|A}} - is a homeomorphism between {{M|A}} and {{M|f(A)\s
  708 B (124 words) - 13:24, 7 March 2017
• NeedEditingSpace
  ...the covering is [[homeomorphic]] to {{M|U}} via the [[restriction onto its image]] of the {{link|covering map|topology}}</ref>
  5 KB (881 words) - 16:24, 2 March 2017
• Exercises:Saul - Algebraic Topology - 9/Exercise 9.7
  Let {{M|p\in\crp}} be the apex of the cone, {{ie}} the image of {{M|\mathbb{RP}^2\times\{1\} }} under the the cone's [[quotient topology ...\rightarrow\mathbb{B}^3}} which takes an [[open neighbourhood]] of {{M|x}} onto the [[open unit ball]] at the origin.
  8 KB (1,299 words) - 13:33, 15 March 2017