What does this mean: "{-π,π}⊆u"? What is "π"? Does this simply mean that U is in the topology if and only if any time x is in U, -x is also? In that case, these questions are close to trivial!blbl said:consider (ℝ,τ) , where τ={∅}∪{u⊆ℝ:{-π,π}⊆u}.
Is [-4.4] open in (ℝ,τ) ? Justify your answer
Is (-3,3) closed in (ℝ,τ) ? Justify your answer
No, [-4.4] is not a part of the set (ℝ,τ) as it is a single point and not an interval.
Yes, (-3,3) is a part of the set (ℝ,τ) as it is an open interval that includes all real numbers between -3 and 3.
The set (ℝ,τ) is open as it contains only open intervals and does not include the endpoints.
[-4.4] is neither open nor closed in (ℝ,τ) as it is a single point and not an interval.
(-3,3) is open in (ℝ,τ) as it does not include the endpoints -3 and 3.