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 -complex and a space in order that be an absolute co-extensor for . Then we prove the existence of and describe a wedge representative of extension dimension for spaces in a wide class relative to polyhedra or -complexes. We also obtain a result on the existence of a “countable” representative of the extension dimension of a Hausdorff compactum.
Ivan IVANŠIĆ. Leonard R. RUBIN. "Extension dimension of a wide class of spaces." J. Math. Soc. Japan 61 (4) 1097 - 1110, October, 2009. https://doi.org/10.2969/jmsj/06141097