Contracting homotopy

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Definition

Let X be a topological space. A contracting homotopy for X is a homotopy F: X \times I \to X such that there exists a point x_0 \in X such that:

  • F(x,0) = x \ \forall \ x \in X
  • F(x,1) = x_0 \ \forall \ x \in X

A topological space which has a contracting homotopy is termed a contractible space.