Authors: Arnautov Vladimir, G.N. Ermakova
Abstract
For any countable field $ R $ and any non-discrete metrizable field
topology $ \tau _0 $ of the field, the lattice of all field topologies of the field
admits:
\newline
-- Continuum of non-discrete metrizable field topologies of the field stronger
than the topology $ \tau _0 $ and such that $ \sup \{\tau
_1, \tau _2 \} $ is the discrete topology for any different
topologies;
\newline
-- Continuum of non-discrete metrizable field topologies of the field stronger
than $ \tau _0 $ and such that any two of these topologies are
comparable;
\newline
-- Two to the power of continuum of field topologies of the field stronger
than $ \tau _0 $, each of them is a coatom in the lattice of
all topologies of the field.
V.I. Arnautov
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
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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