Consider the topology on ℤ with basis {S(a, b) : a, b ∈ ℤ and a ≠ 0}, where S(a, b) = {an + b : n ∈ ℤ}.
Consider the following statements.
I. S(a, b) is both open and closed for each a, b ∈ ℤ with a ≠ 0.
II. The only connected set containing x ∈ ℤ is {x}.
Which one of the following is correct?
1
Both I and II are TRUE
2
I is TRUE and II is FALSE
3
I is FALSE and II is TRUE
4
Both I and II are FALSE