How can I formally express a function that I explain?

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Assume that there are $26$ points $s_1, s_2, \ldots, s_5, d, n_1, n_2, \ldots, n_{20}$, where $s_i$'s are source points, $d_1$ is a destination point, $n_i$'s are normal points.

Let us denote the position of source point $s_i$'s by $p_{s_i}$.

Let us denote the position of destination point $d$'s by $p_{d}$.

Let us denote the position of normal points $n_i$'s by $p_{n_i}$.

All positions are in $\mathbb{R}^2$.

For example, $p_{s_1}=(1,0),~\ldots,~p_{n_{20}}=(50, 30)$.


I want to express a function $f$ whose inputs are a set of points of all points and whose output is a set of vectors of some points (a path from each source to its corresponding destination).

For example, $$f(p_{s_1},\ldots,p_{s_5},p_{d},p_{n_1},\ldots,p_{n_{20}})=\{f_{s_1}, f_{s_2}, f_{s_3}, f_{s_4}, f_{s_5}\},$$ where $f_{s_i}=(p_{s_i},\ldots,p_{d})$ for all $i\in\{1,2,3,4,5\}$. Here, '$\dots$' are normal nodes arbitrarily determined according to a specific rule.

In this case, the function $f$ is defined by $$ f:\mathbb{R}^{2\times26} \to ???. $$

I want to define this function, but it is too hard to express in formal paper. If someone know how to express this function, please let me know, thank you.

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Denote by $N$ your set of 20 normal nodes, and by $N^k$, the $k$-fold cartesian product of $N$ with itself. Now define $\mathcal N$ as $$\mathcal N = N \cup N^2 \cup N^3 \cup \cdots$$ Now your function $f$ must be on the same domain you have given, but the codomain should be $\mathcal N$.

Suppose, for example, $f(s_2)$ is an element of $N^7$, this means this function selects a path from $f_{s_2}$ to $p_d$ having 7 intermediate normal nodes. I hope my understanding of your question is correct.