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IMI/Publicaţii/BASM/Ediţii/BASM n.1(95)-n2(96), 2021/

On non-discrete topologization of some countable skew fields

Authors: Arnautov Vladimir, G., N., Ermakova

Abstract

If for any finite subset $M$ of a countable skew field $ R $ there exists an infinite subset $ S\subseteq R $ such that $r\cdot m=m\cdot r$ for any $r\in S $ and for any $m\in M$, then the skew field $ R $ admits: \newline-- A non-discrete Hausdorff skew field topology $ \tau _0 $. \newline -- Continuum of non-discrete Hausdorff skew field topologies which are 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 $; \newline -- Continuum of non-discrete Hausdorff skew field topologies which are stronger than $ \tau _0 $ and such that any two of these topologies are comparable; \newline -- Two to the power of continuum Hausdorff skew field topologies stronger than $ \tau _0 $, and each of them is a coatom in the lattice of all skew field topologies of the skew fields.

V. I. Arnautov
Institute of Mathematics and Computer Science
Chisinau, Moldova
E-mail:

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