Difference between revisions of "Deformation retraction/Definition"

Revision as of 20:08, 11 May 2016

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]

Caution:Be sure to see the warnings on terminology

References

1. ↑ ^{1.0 1.1} An Introduction to Algebraic Topology - Joseph J. Rotman