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- Jan 26, 2012

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**Problem**: Show that the following spaces are homotopy equivalent:\[\mathbb{R}^3\backslash\{\text{two lines through the origin}\} \simeq S^2\backslash\{\text{four points}\}\ \simeq \mathbb{R}^2\backslash\{\text{three points}\}\simeq S^1\vee S^1\vee S^1.\]

Note that the last space ($S^1\vee S^1\vee S^1$) is a one point union of three circles.

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