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In mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle S^{1}} , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers
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displaystyle group circle mathbb complex number unit isomorphic pi numbers multiplication angle theta times rotation compact subgroup two fourier representations
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Circle group | is a | closed subgroup of C | 0.90 | text |
| Circle group | is a | fundamental starting point in the study of ergodic theory and dynamical systems | 0.90 | text |
| Circle group | is a | divisible group | 0.90 | text |
| Circle group | is a | kernel of the norm homomorphism N C / R | 0.90 | text |
| Circle group | is a | hyperfinite cyclic group C N | 0.90 | text |
| Riemann surfaces | instance of | Line bundles and gauge theoryThe circle group appears naturally in the theory of Hermitian complex line bundles over manifolds and algebraic varieties | 0.80 | text |
| Circle group | related to Abstract group structure | The | 0.60 | section |
| Circle group | related to Abstract group structure | Its | 0.60 | section |
| Circle group | related to Algebraic group structure | The | 0.60 | section |
| Circle group | related to Algebraic group structure | Equivalently | 0.60 | section |
| Circle group | related to Algebraic group structure | In | 0.60 | section |
| Circle group | related to Conventions | While | 0.60 | section |
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