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The free abelian topological group as a subgroup of the free locally convex topological vector space
Journal of Group Theory, 2003An invariant pseudometric \(\rho\) on an abelian group \(G\) is said to have the Enflo property provided \(\forall_{x\in G}[\rho(x^2,e)=2\rho(x,e)].\) It is proved that a Hausdorff abelian group can be embedded as a topological subgroup in a locally convex Hausdorff topological vector space \(\Leftrightarrow\) the topology of \(G\) is generated by a ...
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Elementary theories of complete torsion-free Abelian groups with p-ary topology
Mathematical Notes of the Academy of Sciences of the USSR, 1973The complete torsion-free Abelian groups are investigated as dibasic RPC models whose second basic set comprises subgroups forming a chain with factors of order p. Two theorems about the elementary theories of classes of such models are proved.
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A Free Subgroup of the Free Abelian Topological Group on the unit Interval
Bulletin of the London Mathematical Society, 1982Katz, Eli +2 more
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A group topology on the free abelian group of cardinality c that makes its square countably compact
Fundamenta Mathematicae, 2011Ana Carolina Boero +1 more
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