On the number of topologies on countable fields
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2019-09-24 15:07
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515.12+515.14+515.16 (1)
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SM ISO690:2012
ARNAUTOV, Vladimir; ERMACOVA, Galina. On the number of topologies on countable fields. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 1(89), pp. 79-90. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 1(89) / 2019 / ISSN 1024-7696

On the number of topologies on countable fields


CZU: 515.12+515.14+515.16
MSC 2010: 22A05.
Pag. 79-90

Arnautov Vladimir1, Ermacova Galina2
 
1 Vladimir Andrunakievich Institute of Mathematics and Computer Science,
2 Moldova Tiraspol State University
 
Disponibil în IBN: 16 august 2019


Rezumat

For any countable field R and any non-discrete metrizable field topology 0 of the field, the lattice of all field topologies of the field admits: – Continuum of non-discrete metrizable field topologies of the field stronger than the topology 0 and such that sup{1, 2} is the discrete topology for any different topologies; – Continuum of non-discrete metrizable field topologies of the field stronger than 0 and such that any two of these topologies are comparable; – Two to the power of continuum of field topologies of the field stronger than 0, each of them is a coatom in the lattice of all topologies of the field.

Cuvinte-cheie
Countable field, topological fields, Hausdorff topology, basis of the filter of neighborhoods, number of topologies on countable field, lattice of topologies on field