11 citations · 11 across the 4 of their papers we have counts for
4 papers
Extending homeomorphisms on Cantor cubes
E. Shchepin, V. Valov
We discuss the question of extending homeomorphism between closed subsets of the Cantor discontinuum . It is established that any homeomorphism between two closed subsets…
Local section of Serre fibrations with 3-manifold fibers
N. Brodsky, A. Chigogidze, E. V. Shchepin
It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. An exte…
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…
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…