Topological retraction

Deformation retraction

Let be a subspace and the inclusion. A deformation retraction is a is a retraction, i.e. , such that #m/def/homotopy

Hence in , is a left inverse of , but in Naïve homotopy category is a proper inverse of .

Properties

• Clearly if is a deformation retract of , . Thus a deformation retraction is a stronger kind of Homotopy equivalence.

#state/tidy | #lang/en | #SemBr