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On vector spaces and algebras with maximal locally pseudoconvex topologies

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Kokk A., Żelazko W.

Studia Mathematica

1994-1995

tom 112

nr 2

195-201

Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological algebras, considering the problem of uniqueness of a complete topology for semitopological algebras and giving an example of a complete locally convex commutative semitopological algebra without multiplicative linear functionals, but with every separable subalgebra having a total family of such functionals.

Ograniczanie wyników

1 Studia Mathematica

1 Kokk A.

1 Żelazko W.

1 1995

Wyniki wyszukiwania

On vector spaces and algebras with maximal locally pseudoconvex topologies