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2009, vol. 61, br. 1, str. 25-52
Finite dimensions modulo simplicial complexes and an R-compacta
(naslov ne postoji na srpskom)
Moscow State University, Russia

Ključne reči: dimension; simplicial complex; AN R-compactum; extension theory
Sažetak
(ne postoji na srpskom)
New dimension functions G-dim and R-dim, where G is a class of finite simplicial complexes and R is a class of AN R-compacta, are introduced. Their definitions are based on the theorem on partitions and on the theorem on inessential mappings to cubes, respectively. If R is a class of compact polyhedra, then for its arbitrary triangulation τ, we have Rτ - dim X = R- dim X for an arbitrary normal space X. To investigate the dimension function R-dim we apply results of extension theory. Internal properties of this dimension function are similar to those of the Lebesgue dimension. The following inequality R-dim X ≤ dim X holds for an arbitrary class R. We discuss the following Question: When R-dim X < ∞ → dim X < ∞? AMS Subject Classification : 54F45, 55M10.
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