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edited Nov 13, 2010 at 0:02

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Space-discriminating injective curve

Let $f\colon \mathbb R^1\to \mathbb R^3$ be a continuous and injective map. Is $\mathbb R^3\setminus f(\mathbb R^1)$ a path-connected space?

at.algebraic-topology dg.differential-geometry mg.metric-geometry gt.geometric-topology

asked Nov 12, 2010 at 23:57

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