K Maximum Notation

Question

Suppose I have an unordered set $U = \{u_1, u_2, u_3, ..., u_n\}$. What is the right notation for the $k$ $u_i \in U$ that maximizes $f: U \rightarrow \mathbb{R}$? I use this notation when $k=1$:

$$ \textrm{argmax}_{u_i \in U} f(u_i)$$

Answer 1

How about $f^{-1}(\max(\mathrm{ran}(f))?$