Abstract
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.
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Arnautov, V.I., Filippov, N.M. On Prebox Module Topologies. Mathematical Notes 74, 12–17 (2003). https://doi.org/10.1023/A:1025054729911
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DOI: https://doi.org/10.1023/A:1025054729911