Vector Space with Trivial Dual How to construct a Vector Space $E$ (non trivial) such that, the only continuous linear functional in $E$ is the function $f=0$?

In addition to what Asaf has written: There are non-trivial topological vector spaces with non-trivial topologies which have a trivial dual. I think in Rudin's "Functional Analysis" it is shown that the $L^p$-spaces with $0<p<1$ are an example of this.
