Q20·Section II (Mathematics)·20 of 145The topologist's sine curve: connected but not path connectedLet A={(x,y)∈R2:x=0,−1≤y≤1}A=\{(x,y)\in\mathbb{R}^2:x=0, -1\le y\le1\}A={(x,y)∈R2:x=0,−1≤y≤1}, B={(x,y)∈R2:0<x≤1π,y=sin1x}B=\{(x,y)\in\mathbb{R}^2:0<x\le\tfrac1\pi, y=\sin\tfrac1x\}B={(x,y)∈R2:0<x≤π1,y=sinx1} and X=A∪BX=A\cup BX=A∪B. Then: OptionsAX is connected and path connectedBX is connected but not path connectedCX is not connected but path connectedDX is neither connected nor path connectedPick an option to check your answer.Show answerShow solution Report a problem with this question← Q19All questionsQ21 →Keyboard: A–D answer · S solution · ←/→ previous/next