Topologists's Sin Curve

The Topologist's Sin Curve is well known continuum which is not arcwise connected. The continuum is defined by the union

$$\{(x,y) \in R^2 : 0 < x \le 1 , y=\sin(1/x)\} \cup \{(0,y) \in R^2 : -1 \le y \le 1 \} \quad .$$

It has just two path components. More we can find in [74, p.137] .

Topologists's Sin Curve- fig. a


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