Proof That Any Two Paths in the Plane are Homotopic
Any two paths inare homotopic.
A continuous function fruntion the closed intervalinto a spaceis called a path in
The spacewith the product topology is a normal space and its subsetis closed in the space.
Ifis any continuous function from A intothen by Tietze's Extension Theorem, f has continuous extension
Hence any two paths inare homotopic.