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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
MSC:
 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