What do the mu and (.) symbol represent in the deterministic/policy formula? I am currently going through the OpenAI Spinning Up documents and the following notation puzzled me. What do the mu and . sign mean in the following two formulas?

 A: Using a dot in a function lets us unambiguously fill in some arguments but leave others free, with the free arguments being the ones with dot(s). A simpler example of this kind of thing would be like if we had $f : \mathbb R^2 \to \mathbb R$ given by
$$
f(x, y) = x^2y
$$
and I wanted to talk about the function that results from filling in $y = 2$ but with $x$ still free, I could refer to $f(\cdot, 2)$.
In this particular example, $\pi(\cdot|s_t)$ indicates that we still mean a whole density, but we're conditioning on $s_t$. Doing something like $\pi(a|s_t)$ to refer to the density would be an abuse of notation (albeit a common one) since technically this is just a single number now rather than being a function.
As for $\mu(s_t)$, it looks like $\mu$ is a deterministic function mapping the state $s_t$ at time $t$ to the policy $a_t$ at time $t$. If you're used to seeing $\mu$ as a real-valued parameter or something like that then this might look weird, but here $\mu$ is just denoting a fixed function. 
