Properties of final unrefinable chains of groups topologies
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ARNAUTOV, Vladimir. Properties of final unrefinable chains of groups topologies. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2010, nr. 2(63), pp. 3-19. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(63) / 2010 / ISSN 1024-7696 /ISSNe 2587-4322

Properties of final unrefinable chains of groups topologies

Pag. 3-19

Arnautov Vladimir
 
Institute of Mathematics and Computer Science ASM
 
 
Disponibil în IBN: 16 decembrie 2013


Rezumat

Let G be a nilpotent group and (M,<) be the lattice of all group topologies or the lattice of all group topologies in each of which the group G possesses a basis of neighborhood of unit consisting of subgroups. If  and  ′ are group topologies from M such that  = 0 ≺M 1 ≺M . . . ≺M n =  ′, then k ≤ n for any chain  =  ′ 0 <  ′ 1 < . . . <  ′ k =  ′ of topologies from M.

Cuvinte-cheie
Topological groups, modular lattice,

lattice of group topologies, chain of topologies, unrefinable chain