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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, номер 1, страницы 63–74
(Mi basm523)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Research articles
On the number of topologies on countable skew fields
V. I. Arnautova, G. N. Ermakovab a Vladimir Andrunachievici Institute of Mathematics and Computer Science, 5 Academiei str., MD-2028, Chisinau Moldova
b Transnistrian State University, 25 October str., 128, Tiraspol, 278000 Moldova
Аннотация:
If a countable skew field $ R $ admits a non-discrete metrizable topology $ \tau _0 $, then the lattice of all topologies of this skew fields admits:
– Continuum of non-discrete metrizable topologies of the skew fields stronger than the topology $ \tau _0 $ and such that $ \sup \{\tau _1, \tau _2 \} $ is the discrete topology for any different topologies $ \tau_1$ and $\tau _2 $;
– Continuum of non-discrete metrizable topologies of the skew fields stronger than $ \tau _0 $ and such that any two of these topologies are comparable;
– Two to the power of continuum of topologies of the skew fields stronger than $ \tau _0 $, each of them is a coatom in the lattice of all topologies of the skew fields.
Ключевые слова и фразы:
countable skew fields, topological skew fields, Hausdorff topology, basis of the filter of neighborhoods, number of topologies on countable skew fields, lattice of topologies on skew fields.
Поступила в редакцию: 28.01.2020
Образец цитирования:
V. I. Arnautov, G. N. Ermakova, “On the number of topologies on countable skew fields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 63–74
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm523 https://www.mathnet.ru/rus/basm/y2020/i1/p63
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