Proof That Any Two Paths in the Plane are Homotopic

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Theorem

Any two paths inare homotopic.

Proof

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.