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Extension dimension and quasi-finite CW-complexes

Alex Karasev·Vesko Valov
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Abstract

We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We 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. Further, we extend the definition of UV(L)-spaces on non-compact case and show that some properties of UV(n)-spaces and UV(n)-maps remain valid, respectively, for UV(L)-spaces and UV(L)-maps.

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Alex Karasev, Vesko Valov. 2004-05-11. Extension dimension and quasi-finite CW-complexes. https://arxiv.org/abs/math/0405199

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