In the enclosed paper, we will
prove, among others, the following results: (a) A sufficient condition that a space
L be an absolute extensor for the class of stratifiable spaces in that L be
hyperconnected (this is a refinement of the concept of equiconnected space). This
condition is also necessary if L is a metrizable space. (b) Every hypogeodesic space is
hyperconnected. (o) Every equiconnected space is ∞-hyperconnected. (d) Every
∞-hyperconnected space is an absolute extensor for the class of CW-complexes of
Whitehead.