We establish the following characterization of the approximable dimension of the metric space X with respect to the commutative ring R with identity: a-dimR X ≤ n if and only if there exist a metric space Z of dimension at most n and a proper UVn-1-mapping f : Z → X such that Ȟn(f-1(x); R) = 0 for all x ∈ X. As an application we obtain some fundamental results about the approximable dimension of metric spaces with respect to a commutative ring with identity, such as the subset theorem and the existence of a universal space. We also show that approximable dimension (with arbitrary coefficient group) is preserved under refinable mappings.
|出版ステータス||Published - 1997 12月 1|
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