Difference between revisions of "Topological retraction"

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m (Alec moved page Retraction to Topological retraction without leaving a redirect: Retraction is a thing in category theory too)
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Revision as of 08:04, 13 December 2016

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Demote to grade A once tidied up. Find other sources. Be sure to link to deformation retraction and strong deformation retraction

Definition

Retraction/Definition
Claim 1:

  • This is equivalent to the condition: [ilmath]r\circ i_A=\text{Id}_A[/ilmath] where [ilmath]i_A[/ilmath] denotes the inclusion map, [ilmath]i_A:A\hookrightarrow X[/ilmath] given by [ilmath]i_A:a\mapsto x[/ilmath]

TODO: In the case of [ilmath]A=\emptyset[/ilmath] - does it matter? I don't think so, but check there is nothing noteworthy about it. Also proof of claims


See also

Important theorems

Lesser theorems

References