Is $\mathbb R^2 \setminus ( [0,\infty)\times \{0\}) $ simply connected ? My guess is it is , but I can only show it is path connected , apart from that I am stuck . Please help . Thanks in advance
2026-03-29 04:34:12.1774758852
Is $\mathbb C \setminus [0,\infty)$ simply connected?
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Hint. $$ (x,y)\in\mathbb R^2 \mapsto -(e^x+iy)^2 \in \mathbb C\setminus[0,\infty)$$ is a homeomorphism.