Extension dimension and quasi-finite CW-complexes. (English) Zbl 1177.54016
Summary: We extend the definition of quasi-finite complexes from countable complexes to arbitrary ones and provide a characterization of quasi-finite complexes in terms of \(L\)-invertible maps and dimensional properties of compactifications. Several results related to the class of quasi-finite complexes are established, such as completion of metrizable spaces, existence of universal spaces and a version of the factorization theorem. Furthermore, we define \(UV(L)\)-spaces in the realm of metrizable spaces and show that some properties of \(UV(n)\)-spaces and \(UV(n)\)-maps remain valid for \(UV(L)\)-spaces and \(UV(L)\)-maps, respectively.
MSC:
| 54F45 | Dimension theory in general topology |
| 55M10 | Dimension theory in algebraic topology |
| 54C65 | Selections in general topology |
Keywords:
extension dimension; cohomological dimension; absolute extensor; universal space; quasi-finite complexReferences:
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