<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">The \h {Topologist's Sin Curve} is well known
\g{continuum} which is not \g{arcwise connected}.  The continuum is defined
by the union
$$
\{(x,y) \in  R^2 : 0 &lt; x \le 1 , y=\sin(1/x)\} \cup
\{(0,y) \in  R^2 : -1 \le y \le 1 \} \quad .
$$
It has just two path components. More we can find in
\cite[p.137]{steen1978} .
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