set $\displaystyle \{(x,x\sin(\frac{1}{x})) : x\in (0,\infty)\} \cup \{(0,0)\} $

subset of R2

is this set path connected?

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- Nov 2nd 2008, 07:47 AMszpengchaois this set path-connected
set $\displaystyle \{(x,x\sin(\frac{1}{x})) : x\in (0,\infty)\} \cup \{(0,0)\} $

subset of R2

is this set path connected?