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.
Негізгі бет Circle and punctured plane homotopy equivalence
Пікірлер: 3