Solenoid (mathematics)

This page discusses a class of topological groups. For the wrapped loop of wire, see Solenoid.

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

where each S_i is a circle and f_i is the map that uniformly wraps the circle S_i+1 n_i times (n_i ≥ 2) around the circle S_i. This construction can be carried out geometrically in the three-dimensional Euclidean space R. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.