# What this “resp.” means?

I’m not a native English speaker and not a good math reader too. My question came while I reading this Debreu article about a existence of a real function to represent the preferences and I’m stuck in this passage:

If $$A$$, $$B$$ are two $$f$$-sets (resp. $$i$$-sets) and $$A \cap B$$ is not empty, then $$A \cup B$$ is an $$f$$-set (resp. $$i$$-set).

What’s this “resp.” means?

It abbreviates the word respectively. In this context it means that two results are being stated simultaneously:

• if $$A,B$$ are two $$f$$-sets, and $$A\cap B\ne\varnothing$$, then $$A\cup B$$ is an $$f$$-set; and
• if $$A,B$$ are two $$i$$-sets, and $$A\cap B\ne\varnothing$$, then $$A\cup B$$ is an $$i$$-set.

In other words, read it first without the parenthetical items, and then read it again with the parenthetical items substituted for the items immediately before them.

Resp. is an abbreviation for respectively.

What was written there is a shorter way of saying the following.

If $$A,B$$ are two f-sets and $$A\cap B$$ is not empty, then $$A\cup B$$ is an f-set.

If $$A,B$$ are two i-sets and $$A\cap B$$ is not empty, then $$A\cup B$$ is an i-set.