What is the meaning of (resp. closed) in set theory?

Question

I'm sure this a spectacularly basic question but I can't seem to find the definition of this anywhere.
Here's some context:

If $U$ and $V$ are open (resp. closed) then $U\cup V$ is open (resp. $U\cap V$ is closed). If $\left\{U_{i}\right\}_{i=1}^{\infty}$ is a countable collection of open sets, must $\bigcap_{i\in I} U_{i}$ be open? Provide a proof or counterexample. Similarly, if $\left\{A_{i}\right\}_{i\in I}$ is an infinite collection of closed sets, must $\bigcap_{i\in I} A_{i}$ be closed?

Answer 1

Here, "resp." is an abbreviation for "respectively". So:

If $U$ and $V$ are open (resp. closed) then $U\cup V$ is open (resp. $U\cap V$ is closed).

means:

If $U$ and $V$ are open (respectively closed) then $U\cup V$ is open (respectively $U\cap V$ is closed).

which is a lazy way to write:

If $U$ and $V$ are open then $U\cup V$ is open. If $U$ and $V$ are closed then $U\cap V$ is closed.