Representation of algebra on a space of functions on real line with discrete topology

[xboy]

So suppose I have a Lie Algebra. Now I want to represent it on a space of square integrable functions on real line with discrete topology. For instance take the 1-d translation group. We can represent it on the space of functions on the real line with the usual topology by the operator d/dx. But if I have a discrete topology d/dx can't be the representation. So can I always represent it and how would I do it in this case?