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IMI/Publicaţii/BASM/Ediţii/BASM n.1(89), 2019/

On the number of topologies on countable fields

Authors: Arnautov Vladimir, G.N. Ermakova

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: \newline -- 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; \newline -- Continuum of non-discrete metrizable field topologies of the field stronger than $ \tau _0 $ and such that any two of these topologies are comparable; \newline -- 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.

V.I. Arnautov
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail:

G.N. Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
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