Extension dimension of a wide class of spaces

Abstract

We prove the existence of extension dimension for a much expanded class of spaces. First we obtain several theorems which state conditions on a polyhedron or $\mathrm{CW}$-complex $K$ and a space $X$ in order that $X$ be an absolute co-extensor for $K$. Then we prove the existence of and describe a wedge representative of extension dimension for spaces in a wide class relative to polyhedra or $\mathrm{CW}$-complexes. We also obtain a result on the existence of a “countable” representative of the extension dimension of a Hausdorff compactum.