Woit · §7.4 Complex projective space
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The passage names RP^1 the real projective line and describes its line-through-the-origin model.
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Figure 7.1: The real projective line
One sees that each such line hits the unit circle in two opposite points, so this set could be parametrized by a semi-circle, identifying the points at the two ends. This space is given the name and called the “real projective .