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Definition 155

[0Y4]We denote by \(ℝ/2πœ‹\) the quotient space \(ℝ/∼\) where \(x∼ y\iff (x-y)/(2πœ‹)βˆˆβ„€\) is an equivalence relation that makes points equivalent that are an integer multiple of \(2πœ‹\). This space \(ℝ/2πœ‹\) is called the space of real numbers modulo \(2πœ‹\).

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  • \( ℝ /2\pi \)
  • relation, equivalence ---, for \( S^1\)
  • circle
  • metric space
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