# ordered set notation in functions

Do please forgive me, if this question is a duplicate.

How does one correctly notate a function $f$, which takes a ordered subset $S$ from the field $\mathbb{K}$ and returns an other (ordered) subset from the same field in question?

Obviously, the notation $f:S \mapsto T : \text{ ...} \qquad (S,T \subseteq \mathbb{K})$ is invalid, as the function would now take one element from the subset $S$ instead of the subset itself.

I believe, that the correct representation of a ordered set/list would be a tuple $a := (a_1, a_2, .... , a_n) \in \mathbb{K}^n$, but my issue with the function $f$ is, that the tuple size $n$ is not always defined.

This is not a specific task/problem, where I need the notation requested - it is more out of general interest.

$$f:\mathcal{P}(\mathbb{K})\to \mathcal{P}(\mathbb{K})$$ Where $\mathcal{P}(\mathbb{K})$ denotes the power set of $\mathbb{K}$.