Some topics on the continuation and smoothing of vector functions

We consider problems of continuation of vector functions from a subspace to the entire space and of smoothing problems for these functions. It is shown that there exists a reflexive separable spaceX and a subspaceY such that even a very smooth mapping ofY does not extend to a uniformly continuous mapping of a neighborhood ofY.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 906–916, December, 1995.