Deformation retraction/Definition

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Definition

A subspace, [ilmath]A[/ilmath], of a topological space [ilmath](X,\mathcal{ J })[/ilmath] is called a deformation retract of [ilmath]X[/ilmath], if there exists a retraction[1], [ilmath]r:X\rightarrow A[/ilmath], with the additional property:

  • [ilmath]i_A\circ r\simeq\text{Id}_X[/ilmath][1]
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References

  1. 1.0 1.1 An Introduction to Algebraic Topology - Joseph J. Rotman