Metrizability of locally compact vector spaces

Seth Warner
1971 Proceedings of the American Mathematical Society  
By use of the theory of characters and the Pontryagin-van Kampen theorem, it is shown that if £ is a locally compact vector space over a discrete division ring K of characteristic zero and if dim^Ti <2m, where m is the cardinality of K, then E is metrizable.
doi:10.1090/s0002-9939-1971-0270114-x fatcat:3rmxrvmpbbaotbkhcsz5mefg5y