Q: Describe S¹ as quotient of [0,1]. What is the quotient map? Identify 0 ~ 1: q: [0,1] → S¹, q(t) = e^(2πit). q(0) = q(1) = 1: glues endpoints! Quotient topology: U open ⟺ q⁻¹(U) open. S¹ ≅ [0,1]/(0~1)! (Torus: square with edges glued!)