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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…
math.GT1999
Menger (Nobeling) manifolds versus Hilbert cube (space) manifolds - a categorical comparison
Alex Chigogidze, V. V. Fedorchuk
We show that the n-homotopy category of connected (n+1)-dimensional Menger manifolds is isomorphic to the homotopy category of connected Hilbert cube manifolds whose k-dimensional…