Hopf bundles and n-soft dimension-raising mappings
Using the well-known Hopf bundles, the author sketches a proof of the following theorem for \(n=1:\) For \(n=1,3,7\) there exist an \((n+1)\)- dimensional compact metric space \(X_ n\) and an n-soft mapping \(g_ n:X_ n\to Q\), where \(X_ n\) is the limit of an inverse sequence \(S_ n=\{M_ i,f_ i^{i+1}\}\), \(M_ i\) are Q-manifolds and \(g_ n\) is the projection of \(X_ n\) onto \(M_ 1=Q\). Moreover, each set \((f_ i^{i+1})^{-1}(x)\) is either a point or the (topological) sphere \(S^ n\).
scientific article; zbMATH DE number 3955954