engleski

Extension dimension of a wide class of spaces

We prove the existence of extension dimension for a much extended class of spaces. First we obtain several theorems which state conditions on a polyhedron or a CW-complex <i>K</i> and a space <i>X</i> in order that <i>X</i> be an absolute co-extensor for <i>K</i>. Then we prove the existence of and describe a wedge representative of extension dimension for spaces in a wide class relative to polyhedra or CW-complexes. We also obtain a result on the existence of a "countable" representative of the extension dimension of a Hausdorff compactum.

absolute co-extensors; absolute extensors; anti-basis; cardinality of a complex; CW-complex; dd-space; ddP-space; extension dimension; extension theory; extension type; polyhedron; pseudo-compact; weak extension dimension; weight.

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