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In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms (Si, fi), fi: Si+1 → Si, i ≥ 0, where each Si is a circle and fi is the map that uniformly wraps the circle Si+1 ni times (ni ≥ 2) around the circle Si. This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.

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  • Solenoid (mathematics)
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  • In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms (Si, fi), fi: Si+1 → Si, i ≥ 0, where each Si is a circle and fi is the map that uniformly wraps the circle Si+1 ni times (ni ≥ 2) around the circle Si. This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.
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  • S/s086040
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  • Solenoid
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  • In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms (Si, fi), fi: Si+1 → Si, i ≥ 0, where each Si is a circle and fi is the map that uniformly wraps the circle Si+1 ni times (ni ≥ 2) around the circle Si. This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group. In the special case where all ni have the same value n, so that the inverse system is determined by the multiplication by n self map of the circle, solenoids were first introduced by Vietoris for n = 2 and by van Dantzig for an arbitrary n. Such a solenoid arises as a one-dimensional expanding attractor, or Smale–Williams attractor, and forms an important example in the theory of hyperbolic dynamical systems.
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