No embeddings of solenoids into surfaces
Boju Jiang, Shicheng Wang, Hao Zheng · Proceedings of the American Mathematical Society · 2008
A quick proof of Bing’s theorem indicated by the title is given. Indeed the inverse limit of a sequence of degree > 1 >1 maps between closed oriented m m -manifolds can never be embedded into any closed orientable ( m + 1 ) (m+1) -manifold. The proof also concludes Gumerov’s result on the covering of solenoids.