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## 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
E-mail:

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