On vector spaces and algebras with maximal locally pseudoconvex topologies
Studia Mathematica, Tome 112 (1995) no. 2, p. 195.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 46H05, 46A16
Mots-clés : maximal -convex topology, complete Hausdorff topological vector space, complete locally pseudoconvex space, topological algebras, complete locally convex commutative semitopological algebra without multiplicative linear functionals 
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     author = {A. Kokk and W. \.Zelazko},
     title = {On vector spaces and algebras with maximal locally pseudoconvex topologies},
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     pages = {195},
     publisher = {mathdoc},
     volume = {112},
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     year = {1995},
     zbl = {0837.46037},
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A. Kokk; W. Żelazko. On vector spaces and algebras with maximal locally pseudoconvex topologies. Studia Mathematica, Tome 112 (1995) no. 2, p. 195. https://geodesic-test.mathdoc.fr/item/STUMA_1995__112_2_216146/