Ans: Is [-4.4] & (-3,3) open/closed in (ℝ,τ)? Justify your answer

[blbl]

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

 

[g_edgar]

Consider [-4,4] ... what do you think the answer should be? What is the definition of "open"? Does this set meet that definition?

 

[HallsofIvy]

consider (ℝ,τ) , where τ={∅}∪{u⊆ℝ:{-π,π}⊆u}.

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!

Is [-4.4] open in (ℝ,τ) ? Justify your answer
Is (-3,3) closed in (ℝ,τ) ? Justify your answer