On the number of group topologies on countable groups
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ARNAUTOV, Vladimir, ERMACOVA, Galina. On the number of group topologies on countable groups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2014, nr. 1(74), pp. 101-112. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1(74) / 2014 / ISSN 1024-7696 /ISSNe 2587-4322

On the number of group topologies on countable groups
CZU: 512.546.6

Pag. 101-112

Arnautov Vladimir1, Ermacova Galina2
 
1 Institute of Mathematics and Computer Science ASM,
2 T.G. Shevchenko State University of Pridnestrovie, Tiraspol
 
 
Disponibil în IBN: 18 iunie 2014


Rezumat

If a countable group G admits a non-discrete Hausdorff group topology, then the lattice of all group topologies of the group G admits:{ continuum c of non-discrete metrizable group topologies such that supf¿1; ¿2g is the discrete topology for any two of these topologies; { two to the power of continuum of coatoms in the lattice of all group topologies.

Cuvinte-cheie
Countable group, group topology, Hausdorff topology, basis of the filter of neighborhoods

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<dc:creator>Arnautov, V.I.</dc:creator>
<dc:creator>Ermacova, G.N.</dc:creator>
<dc:date>2014-02-04</dc:date>
<dc:description xml:lang='en'>If a countable group G admits a non-discrete Hausdorff group topology, then the lattice of all group topologies of the group G admits:{ continuum c of non-discrete metrizable group topologies such that supf¿1; ¿2g is the discrete topology for any two of these topologies; { two to the power of continuum of coatoms in the lattice of all group topologies.</dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 74 (1) 101-112</dc:source>
<dc:subject>Countable group</dc:subject>
<dc:subject>group topology</dc:subject>
<dc:subject>Hausdorff topology</dc:subject>
<dc:subject>basis of the filter of neighborhoods</dc:subject>
<dc:title>On the number of group topologies on countable groups</dc:title>
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