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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