F if x is not an isolated point of s then x is an

(f) If x is not an isolated point of S , then x is an accumulation point of
S .
(g) If α = sup S , then α is an accumulation point of S .
3

3. For each of the following sets, give the interior points, the boundary points, the
accumulation points and the isolated points.
(a) S = ( - 2 , 1) ∪ [0 , 3) ∪ [3 , 10)
S = ( - 2 , 10) : int S = ( - 2 , 10) , bd S = {- 2 , 10 } , S prime = [ - 2 , 10],
no isolated points.
(b) S =
(
[0 , 2) ∩ (1 , 3]
)
∪ {- 1 } ∪ { 5 }
S = (1 , 2) ∪ {- 1 } ∪ { 5 } : int S = (1 , 2) , bd S = {- 1 , 1 , 2 , 5 } , S prime =
[1 , 2], isolated points {- 1 , 5 } .
(c) S = { r ∈ Q | 0 < r <
√
4