/sci/ - Science & Math

I'm learning topology and I don't understand one thing.

Let [math]V[/math] be a normed space for simplicity, and let [math]C[/math] be some set in [math]V[/math]. For some continuous linear functional [math]f: V \to \mathbb{R}[/math], define

[math]\mu = \inf_{x \in C} f(x)[/math].

Now, this means that there is a sequence of [math]\{x_n\}[/math] in [math]C[/math] such that [math]f(x_n)[/math] converges to [math]\mu[/math]... but in what topology? Is this predetermined? Do we fix the topology at some stage? I'm lost about this.