Question

Give an example of an open set which is not an open interval

Answer 1

Answer:

Step-by-step explanation:

The real numbers except zero(0) is one useful example. The generally the union of two disjoint open intervals is not an interval but is an open. Hence, the real numbers except zero(0) is one useful example.

Answer 2

Simply, the union of any two open intervals can be an open set since it doesn't have any boundary or limit, but is not an open interval.

E.g.: The set (-2, -1) ∪ (1, 2) or (-2, 2) - [-1, 1].