I don't know if this is a dumb question but i think i better ask and get my confusion clarified .
Talking about topologies in a Vector space , Topologies induced by norms are pretty easy to understand. The open sets of the topology are the open balls with respect to the norm .
But now its not clear to me how the topology in the dual space will be like , how do the open balls or sets will look like for the continuous functionals in the dual ? and same with the bidual ?
We generally define a norm on the functional , and we define openness using this norm right ? I am sort of not able to imagine or get get the feeling about weak topology or weak star topology .
I would like your suggestions , explanations, recommendation. I really need to understand these things clearly as soon as possible. Thank you for your help. Merry Christmas!