In Automorphic forms on $\operatorname{SL}_2(\mathbb R)$ $\S$11.0 Borel writes the following. $X$ is a Lie group (quotient of $\operatorname{SL}_2(\mathbb R)$ by some group)
Recall that $C^\infty(X)$ [$\mathbb C$-valued functions] is usually viewed as a topological vector space with the topology defined by absolute and uniform convergence on compact sets - that is, by the seminorms $\nu_{D,L}$ ($L$ compact in $X$, $D\in \mathcal U$ [left-invariant differential operators]) - where $$\nu_{D,L}(f) = \max_{x\in L}|Df(x)|$$
There are no series involved, so I'm wondering what the "absolute" stands for. Or does it simply mean that the convergence is uniform for $f$ and its derivatives?