There is another branch of the TVS theory, which is not dead at all. It deals with TVS over non-Archimedean fields. See
C. Perez-Garcia and W. H. Schikhof, Locally Convex Spaces over Non-Archimedean Valued FieldsLocally Convex Spaces over Non-Archimedean Valued Fields, Cambridge University Press, 2010. doi:10.1017/CBO9780511729959