**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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