Consider this question: Let we have a vector space which is infinite dimensional then show that it's dual space is also infinite dimensional.
I have been reading notes on Manifolds from class notes of senior and this was left to do itself.
I have done a course on Linear algebra 2 years ago and followed Hoffman, Kunze but I can't recall now what result I should use and I looked back at it but not sure what result to use. So, can you please give some hints?