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Information × Registration Number 0213U002253, 0112U005004 , R & D reports Title The аlgebraic and topological methods of investigating metric spaces, matrix groups and topological semigroups. popup.stage_title Head Dzhalyuk N, Registration Date 23-01-2013 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 The tower method is adapted for zero dimentional spaces of big weight and is obtained classification of asymptotically zero-dimentional asymptotically homogeneous metric spaces. Asymptotically zero-dimentional homogeneous metric spaces of big wieght was classified using adopted tower method. Result was extended to radial coarse spaces. We established the necessary and sufficient conditions, under which from the association of the diagonal blocks of nonsingular block triangular matrices over commutative principal ideal domains follows that corresponding block triangular factorizations of these matrices are associative. We describe all up to the association block diagonal parallel factorizations of nonsingular block diagonal matrices over commutative principal ideal domains. The sufficient conditions, under which each block diagonal factorization of matrix is the block diagonal parallel factorization, were obtained. The criterion of uniqueness up to the association of such factorizations was established. The bicyclic extensions of a linearly ordered group are constructed and theirs algebraic properties are investigated. It is proved that for a commutative linearly ordered group all non-trivial congruences on the constructed extensions are group congruences if and only if the group is archimedean. The sufficient conditions under which the topological Z-Bruck-Reilly and (Z-Bruck) extension of (semi)topological semigroups admits only the direct sum topology and conditions under which the direct sum topology can be coarsened are given. The topological characterizations for some classes of I-bisimple (semi)topological semigroups are given. It is proved that for every Tychonoff semitopological monoid with zero there exists a unique semiregular pseudocompact Brandt ?0-extension. Product Description popup.authors Джалюк Н.С. Зарічний І.М. Павлик К.П. popup.nrat_date 2020-04-02 Close