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For an analytic curve 
$\gamma :\,\left( a,\,b \right)\,\to \,\mathbb{C}$, the set of values approached by 
$\gamma \left( t \right)$, as 
$t\,\searrow \,\,a$ and as 
$t\,\nearrow \,b$ can be any two continua of 
$\mathbb{C}\,\cup \,\left\{ \infty \right\}$.
