Connectedness

In generative syntax, connectedness is a property which is meant to account for parasitic gap constructions of the type illustrated in (i).

Examples
(i) ''? A person who [[close friends of e] admire t]''

In (i) both e and t take who as their antecedent. This is allowed, because the path from e to who and the path from t to who are connected in a specific way. This type of connection is missing in the example in (ii).

(ii) * A person who you admire t because [[close friends of e] become famous]

Comment
The notion of connectedness has been resolved under the Path Containment Condition.

Link
Utrecht Lexicon of Linguistics