Deformation retraction

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This article defines a property of a homotopy from a topological space to itself

Definition

Let X be a topological space and A a subspace. A deformation retraction from X to A is a homomotopy F: X \times I \to X such that:

  • F(x,0) = x \ \forall \ x \in X
  • F(a,t) = a \ \forall \ a \in A
  • F(x,1) \in A \ \forall x \in X, a \in A

If a deformation retraction exists from X to A, we say that A is a deformation retract of X.

Relation with other properties

Stronger properties

Weaker properties