How to read "Upper closure operator" definition

Question

I a book the "Upper closure operator" definition is given by:

I do understand the concept of the Upper closure operator.

But I cannot figure out how to read the last line.

Could someone explain it?

Thank you.

Answer 1

The bottom line shouldn't start with $P$, since that is already being used for the overall poset being considered. Instead it should be $$Q \mapsto \{y \in P \mid \exists x \in Q : x \le_P y\}.$$