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Homotopy Theory

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Multiple Choice

What is the fundamental group of a space X, denoted by (\pi_1(X))?

  1. The group of all continuous loops in X based at a fixed point.
  2. The group of all continuous maps from the unit circle to X.
  3. The group of all homotopy classes of continuous maps from the unit circle to X.
  4. The group of all continuous maps from X to the unit circle.
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