The Warsaw circle is a compact subset of the plane produced by “closing up” a topologist’s sine curve with an arc: Wikipedia.

The example shows the TikZ native plotting, without pgfplots, and a Bezier curve.

\draw plot[domain=0.01:1, samples=5000] (\x,{sin(1/\x r)});
\draw (0,1) -- (0,-1);
\draw (1,{sin(1 r)}) .. controls (4,{sin(1/4 r)-1.2}) and (0,-3) .. (0,-1);

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