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Q: Show S¹ is a 1-manifold. Give charts. U₁ = S¹\{(1,0)}, φ₁(e^(iθ)) = θ ∈ (0,2π). U₂ = S¹\{(-1,0)}, φ₂(e^(iθ)) = θ ∈ (-π,π). Charts cover S¹! Transition: smooth on overlap! 1-MANIFOLD (locally like ℝ!)! (Every point has interval neighborhood!)