Let $k \in \mathbb{R}$ and: $f(x) = \sin \frac{1}{x}$ , for $x\neq 0$ with $f(0) = k$.For what value(s) of $k$, the graph of $f$ is NOT a connected subset of the plane?
Connected subset of the plane
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general-topology
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9Do you have any thoughts about the likely answer? For example, what do you think happens if $k=17$? If $k=-10583421$? Any difference if $-1\leq k\leq 1$? – 2011-10-03
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3Is this a homework problem? – 2011-10-03
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0Related question: http://math.stackexchange.com/questions/34103/for-a-function-from-mathbbr-to-itself-whose-graph-is-connected-in-mathbbr – 2011-10-03