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Homotopy Theory
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What is the fundamental group of a space X, denoted by (\pi_1(X))?
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A
The group of all homotopy classes of continuous maps from the unit circle to X.
💡 Explanation:
The fundamental group (\pi_1(X)) is defined as the group of all homotopy classes of continuous maps from the unit circle (S^1) to X, where two maps are homotopic if they can be continuously deformed into each other while keeping the endpoints fixed.