When LCS is isomorphic to subspace of some function space? Updated: Following Michael's suggestion, I rephrase the question slightly. 
Given a locally convex (Hausdorff) topological vector space (LCTVS), when is it isomorphic to a subspace of some function space $Y^X$ (equipped with the product topology), where $Y$ is, say, some Banach space (if it helps simplify things, can assume $Y=\mathbb{C}$, the complex field), and $X$ is some set. We are free to choose X and Y. 
If not all LCTVS have this property, then what kind of conditions do we need?
Any reference would be appreciated, thanks!
 A: Yes, every LCTVS can be realized as a function space: every LCTVS is isomorphic to the dual of its dual space equipped with the weak* topology.  This is a consequence of a version of the Hahn-Banach theorem which states that in a real LCTVS two disjoint closed convex sets, one of which is compact, can be strictly separated.  See Section IV.3 of A Course in Functional Analysis by Conway.
A: If I interpret the question correctly, Yaoliang would like to know which LCTVS are isomorphic to $\mathbb{C}^X$, where $X$ is a set (no topology), and $\mathbb{C}^X$ is given the product topology. If this is so, the answer is: very few. Actually, spaces of this form are fully determined by the cardinality of $X$.
Just to make an example: no infinite dimensional normed space can be isomorphic to a space of this form. Indeed, in this case the set $X$ would have to be infinite, but then every neighborhood of $0$ in $\mathbb{C}^X$ would contain a proper vector subspace, and this is never true for normed spaces.
