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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2015, номер 1, страницы 103–114
(Mi basm384)
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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
On the number of ring topologies on countable rings
V. I. Arnautova, G. N. Ermakovab a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., MD-2028, Chisinau, Moldova
b Transnistrian State University, 25 October str., 128, Tiraspol, 278000, Moldova
Аннотация:
For any countable ring $R$ and any non-discrete metrizable ring topology $\tau_0$, the lattice of all ring topologies admits:
– Continuum of non-discrete metrizable ring topologies stronger than the given topology $\tau_0$ and such that $\sup\{\tau_1,\tau_2\}$ is the discrete topology for any different topologies;
– Continuum of non-discrete metrizable ring topologies stronger than $\tau_0$ and such that any two of these topologies are comparable;
– Two to the power of continuum of ring topologies stronger than $\tau_0$, each of them being a coatom in the lattice of all ring topologies.
Ключевые слова и фразы:
countable ring, ring topology, Hausdorff topology, basis of the filter of neighborhoods, number of ring topologies, lattice of ring topologies, Stone-Čech compacification.
Поступила в редакцию: 10.02.2015
Образец цитирования:
V. I. Arnautov, G. N. Ermakova, “On the number of ring topologies on countable rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 1, 103–114
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm384 https://www.mathnet.ru/rus/basm/y2015/i1/p103
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Страница аннотации: | 249 | PDF полного текста: | 48 | Список литературы: | 40 |
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