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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, Number 1, Pages 79–90
(Mi basm502)
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This article is cited in 2 scientific papers (total in 2 papers)
On the number of topologies on countable fields
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
Abstract:
For any countable field $ R $ and any non-discrete metrizable field topology $ \tau _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 $ \tau _0 $ and such that $ \sup \{\tau _1, \tau _2 \} $ is the discrete topology for any different topologies;
– Continuum of non-discrete metrizable field topologies of the field stronger than $ \tau _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 $ \tau _0 $, each of them is a coatom in the lattice of all topologies of the field.
Keywords and phrases:
countable field, topological fields, Hausdorff topology, basis of the filter of neighborhoods, number of topologies on countable field, lattice of topologies on field.
Received: 29.11.2018
Citation:
V. I. Arnautov, G. N. Ermakova, “On the number of topologies on countable fields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 1, 79–90
Linking options:
https://www.mathnet.ru/eng/basm502 https://www.mathnet.ru/eng/basm/y2019/i1/p79
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