I was going through the dual of the basis of a vector space - which is essentially the set of linear functionals such that if $\{\alpha_1,\alpha_2,...,\alpha_n\}$ is the basis vectors then $\{f_1,..,f_n\}$ such that $f_i(\alpha_j)=1$ if $i=j$ or $0$ otherwise. Now I read in Wikipedia which essentially says that dual of anything can be obtained by inverting the conditions (if I understood it correctly)
Now I was wondering will the dual space of all continuous functions,differentiable functions and Riemann integrable functions exist.So will the dual of all Riemann integrable functions be all the differential functions. If they exist then what are they?