https://elib.bsu.by:443/handle/123456789/6614 2026-04-21T13:49:46Z https://elib.bsu.by:443/handle/123456789/344872 Заглавие документа: Axiomatic method of partitions in the theory of N¨obeling spaces. I. Improvement of partition connectivity Авторы: Ageev, S.M. Аннотация: The N¨obeling space N 2k+1 k , a k-dimensional analogue of the Hilbert space, is considered; this is a topologically complete separable (that is, Polish) k-dimensional absolute extensor in dimension k (that is, AE(k)) and a strongly k-universal space. The conjecture that the above-listed properties characterize the N¨obeling space N 2k+1 k in an arbitrary finite dimension k is proved. In the first part of the paper a full axiom system of the N¨obeling spaces is presented and the problem of the improvement of a partition connectivity is solved on its basis. 2007-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344869 Заглавие документа: On extending actions of groups Авторы: Ageev, S.M. Аннотация: Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications. 2010-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344868 Заглавие документа: О продолжении действий групп Авторы: Агеев, С.М. Аннотация: Получены решения проблем плотного и замкнутого продолжения действий компактных групп преобразований. Развитый в работе метод применен к задачам продолжения эквивариантных отображений и построения эквивариантных компактификаций. 2010-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/344862 Заглавие документа: On the exponent of G-spaces and isovariant extensors Авторы: Ageev, S.M. Аннотация: he equivariant version of the Curtis-Schori-West theorem is investigated. It is proved that for a nondegenerate Peano G-continuum X with an action of the compact abelian Lie group G, the exponent exp X is equimorphic to the maximal equivariant Hilbert cube if and only if the free part Xfree is dense in X. We also show that the latter is sufficient for the equimorphy of exp X and Q in the case of an action of an arbitrary compact Lie group G. The key to the proof of these results lies in the theory of the universal G-space (in the sense of Palais). 2016-01-01T00:00:00Z