In topology, intA ∪ A' =? here, A' denotes set of limit points of A

I know that A∪A' = closure of A

and

intA ∪ boundary of A = closure of A

then what about intA ∪ A' = ?
Let $f(A) = A^\circ \cup A'$. We have
$$ f(]0,1[ \cup ]1,2[) = [0,2] = (]0,1[ \cup ]1,2[)^-
$$
while
$$ f(\{0,1\}) = \emptyset
$$
so in general the result varies.
That will be all the interior points and the limit points.  If the set has isolated points they will not be in the union.  That union will be the closure minus the isolated points of A.