Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus \{(0,0)\} $.
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
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general-topology
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12Consider the fundamental groups. It would certainly help to find the answer you're looking for if you gave a little hint at your background. – 2011-04-04