Source: J. Math. Soc. Japan Volume 61, Number 4
(2009), 1097-1110.
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 $\mathop{\mathrm{CW}}$-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 $\mathop{\mathrm{CW}}$-complexes. We also obtain a result on the existence of a “countable” representative of the extension dimension of a Hausdorff compactum.
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Mathematical Reviews (MathSciNet):
MR62423
