equivalent description of "respectively"

Question

I want to define two notions; can we use the notation () to represent "respectively"?

For example: does the statement "A set has (weak) property C if" have the same meaning as "A has (respectively, weak) property C if"?

Answer 1

I'd say it does. For instance, a set $S$ is strongly (resp. weakly) [property] if $S$ satisfies [something] (resp. [something else]).

Or you can drop "resp." entirely, e.g. $f_n$ is said to converge to $f$ strongly (weakly) if $f_n \rightarrow f$ uniformly (pointwise). You can replace the adverb with an adjective as well, e.g. $g_n$ has the strong (weak) boundedness property on $X$ if $g_n$ is uniformly (pointwise) bounded.

I only write this if the strong property 'obviously' implies the weak property, but usually I interpret a sentence like this as saying if I were to replace the word preceding each bracket with the bracketed word then I have another assertion.