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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.
MSC: 22A05 Поступила в редакцию: 28.01.2020
Язык публикации: английский