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
1 ,τ
2 } 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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