We have FiniteDimensional.of_locallyCompactSpace, which is the usual Riesz theorem for normed spaces.
More generally, Bourbaki proves the following: if K is a complete NontriviallyNormedField, then any T2 TVS over K which admits some totally bounded neighborhood of zero is finite dimensional.
We have FiniteDimensional.of_locallyCompactSpace, which is the usual Riesz theorem for normed spaces.
More generally, Bourbaki proves the following: if
Kis a complete NontriviallyNormedField, then any T2 TVS overKwhich admits some totally bounded neighborhood of zero is finite dimensional.