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math.GT2006★ 11 cited
The telescope approach to embeddability of compacta
Sergey A. Melikhov, Evgenij V. Shchepin
We show that an n-dimensional compactum X embeds in R^m, where m>3(n+1)/2, if and only if X x X - Δadmits an equivariant map to S^{m-1}. In particular, X embeds in R^{2n}, n>3, iff…
math.GT2002
Sections of Serre fibrations with low-dimensional fibers
N. Brodsky, A. Chigogidze, E. V. Shchepin
It was proved by H. Whitney in 1933 that it is possible to mark a point in all curves in a continuous way. The main result of this paper extends the Whitney theorem to dimensions 2…