Circle and punctured plane homotopy equivalence

Homotopy is another key concept in topology. This video illustrates homotopy equivalence between a circle (S¹) and a punctured plane (ℝ²\{(0, 0)}). More generally, ℝⁿ\{0} ≃ Sⁿ⁻¹.
Moreover, homotopy equivalent spaces have isomorphic fundamental groups. As a result, fundamental group of a punctured plane is isomorphic to ℤ (additive group of integers), since π₁(S¹) ≅ ℤ.

[ARBB]

I'd suggest making the text a bit cleaner by reducing the size of the full diagram, and putting it aside, highlighting whatever you want to make notice of.