I'm studying the proof of the Riesz representation theorem for regular measures using Real and Complex Analysis of Walter Rudin. In page 38, he introduces some notation that reads:
Notation: We denote $K \prec f$ to mean that $K$ is a compact set (o a topological space), $f \in C(X)$, $f : X \to [0, 1]$ and $f(x) = 1$ for all $x \in K$.
Similarly, we denote $f \prec V$ to mean that $V$ is open, $f \in C(X)$, $f : X \to [0, 1]$ and $\text{supp}(f) \subseteq V$ (support of $f$).
Is there some name for $K \prec f$ and $f \prec V$?
It would be amazing to have some name for $K \prec f$ (like "$f$ is dominated by $V$" or something similar), since it's somewhat cumbersome to talk about this with the instructor without having a name.
I'm not aware of any standard terminology (it's sort of an auxiliary notation in his proof of the Riesz' representation theorem, IIRC), but maybe: $f$ is maximal on $K$ for $K \prec f$ and $f$ is supported in $V$ for $f \prec V$ could be used?