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Hopf bundles and n-soft dimension-raising mappings. (English. Russian original) Zbl 0594.54013
Mosc. Univ. Math. Bull. 40, No. 6, 81-83 (1985); translation from Vestn. Mosk. Univ., Ser. I 1985, No. 6, 101-103 (1985).
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 \(S^ n\).
Reviewer: H.Patkowska
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54F45 Dimension theory in general topology
54B35 Spectra in general topology
54E45 Compact (locally compact) metric spaces