Geodesic
On Prebox Module Topologies
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 12-18

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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. 
@article{MZM_2003_74_1_a1,
     author = {V. I. Arnautov and K. M. Filippov},
     title = {On {Prebox} {Module} {Topologies}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {12--18},
     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a1/}
}
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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/