Ah, I see the problem: The book’s text uses “member” ambiguously.
An intersection type A & B is called an intersection type because the set of values in that intersection type is the intersection of the set of values of type A and the set of values of type B. That is, the members of the intersection type are the values each of which is both a member of set A and a member of set B.
So the name “intersection type” certainly sets the stage for interpreting “member” in that sense (of a value being member of a set).
But then, per your/bishabosha’s interpretation, the text meant to be referring to the other meaning of “member” (i.e., methods, fields, etc., of a type). (Yes, that does seem to be the intent.)
The text should be disambiguated somehow.
I don’t know if there’s a word to put in front of “member” to clarify which kind of member the text means (e.g., corresponding to “set member” for the other kind).
Perhaps it would be clearer to add something like “(methods, etc.)” like this: “The members (methods, etc.) of an intersection type A & B
are all the members of A
and all the members of B
.”
(The union-types page might have the same ambiguity.)