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2008-05-11T19:54:27Z

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{{toposubspace property}}

==Definition==

===Definition with symbols===

A [[subspace]] <math>A</math> of a [[topological space]] <math>X</math> is termed a '''neighbourhood retract''' in <math>X</math> is there is an open subset <math>U</math> of <math>X</math> containing <math>A</math>, such that <math>A</math> is a [[retract]] of <math>U</math>.

==Formalisms==

{{obtainedbyapplyingthe|neighbourhood operator|retract}}

==Relation with other properties==

===Stronger properties===

* [[Strong deformation retract]]
* [[Homotopy retract]]
* [[Retract]]
* [[Open subset]]

==Metaproperties==

{{transitive subspace property}}

If <math>A</math> is a neighbourhood retract of <math>B</math> and <math>B</math> is a neighbourhood retract of <math>C</math>, then we can find a neighbourhood of <math>A</math> in <math>C</math>, for which it is a retract.

{{finite DP-closed subspace property}}

Neighbourhood retract - Revision history

Vipul: 1 revision

Vipul at 22:11, 24 October 2007