homotopy of paths (original) (raw)

Let X be a topological space and p,q paths in X with the same initial point x0 and terminal point x1. If there exists a continuous function F:I×I→X such that

1. 1. F⁢(s,0)=p⁢(s) for all s∈I
2. 1. F⁢(s,1)=q⁢(s) for all s∈I
3. 1. F⁢(0,t)=x0 for all t∈I
4. 1. F⁢(1,t)=x1 for all t∈I

we call F a homotopy of paths in X and say p,q are homotopic paths in X. F is also called a continuous deformation.