Geodesic
On topologization of countably generated algebras
Studia Mathematica, Tome 112 (1994) no. 1, pp. 83-88
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We prove that any real or complex countably generated algebra has a complete locally convex topology making it a topological algebra. Assuming the continuum hypothesis, it is the best possible result expressed in terms of the cardinality of a set of generators. This result is a corollary to a theorem stating that a free algebra provided with the maximal locally convex topology is a topological algebra if and only if the number of variables is at most countable. As a byproduct we obtain an example of a semitopological (non-topological) algebra with every commutative subalgebra topological. 
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W. Żelazko. On topologization of countably generated algebras. Studia Mathematica, Tome 112 (1994) no. 1, pp. 83-88. doi: 10.4064/sm-112-1-83-88

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