Abstract
The classical Eilenberg-Borsuk theorem on extension of partial mappings into a sphere is generalized to the case of an arbitrary complex . It is formulated in terms of extraordinary dimension theory, which is developed in the present paper. When is an Eilenberg-MacLane complex, the result can be expressed in terms of cohomological dimension theory. For partial mappings of an -manifold , the following is obtained: Theorem. If , then there exists a compactum of dimension , such that the mapping extends to and for every abelian group with the cohomological dimension of with coefficients in does not exceed . Thus, in comparison with the classical Eilenberg-Borsuk theorem, there is obtained an additional condition as to the cohomological dimension of . Bibliography: 17 titles.
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