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IMI/Publicaţii/BASM/Ediţii/BASM n.1(92), 2020/

On the number of topologies on countable skew fields

Authors: Arnautov Vladimir, G. N.Ermakova

Abstract

If a countable skew field R admits a non-discrete metrizable topology τ 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 τ 0 and such that sup{τ 12 } is the discrete topology for any different topologies τ 1 and τ 2 ; – Continuum of non-discrete metrizable topologies of the skew fields stronger than τ 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 τ 0 , each of them is a coatom in the lattice of all topologies of the skew fields.

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

G. N. Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:

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