Abstract: In this paper, we consider set-valued mappings jwhose
domain is the product of a space X
with the closed unit interval For a class of such mappings jand nice embedded
subsets A of X,we show that the
“end-point” mappings and have the same selection extension
properties with respect to those pairs of selections for and which are homotopic by a selection
for As a result, we improve known
selection theorems and obtain new ones.
