Geodesic
On Prebox Module Topologies
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 12-18 
V. I. Arnautov; K. M. Filippov. On Prebox Module Topologies. Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 12-18. http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a1/
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     author = {V. I. Arnautov and K. M. Filippov},
     title = {On {Prebox} {Module} {Topologies}},
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     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R$ be a complete topological division ring whose topology is determined by a real-valued valuation, and let $M$ be a vector space over $R$. It is proved that $M$ admits a Hausdorff module topology preceding the box topology in the lattice of all module topologies if and only if the dimension of the vector space $M$ over $R$ is a measurable cardinal.

[1] Arnautov V. I., Filippov K. M., “O predmaksimalnykh topologiyakh na vektornykh prostranstvakh”, Buletinul Academiei de Ştiinţă Republicii Moldova. Matematica, 20:1 (1996), 96–105 | MR

[2] Arnautov V. I., Filippov K. M., “O maksimalnykh tsepyakh v reshetke modulnykh topologii”, Sib. matem. zh., 42:3 (2001), 491–506 | MR | Zbl

[3] Arnautov V. I., Glavatski S. T., Michalev A. V., Introduction to the Theory of Topological Rings and Modules, Marcel Dekker, 1996 | Zbl

[4] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970