Thread: prove that τ is the topology on ℝ

Define τ⊂ P(ℝ) as follows:
τ={φ}∪{u⊆ℝ:{-π,π}⊆u} .
prove that τ is a topology on ℝ .

Originally Posted by blbl

Define τ⊂ P(ℝ) as follows:
τ={φ}∪{u⊆ℝ:{-π,π}⊆u} .
prove that τ is the topology on ℝ .

Is this -\pi,\pi)\subseteq U\right\}" alt="T=\{\varnothing\}\cup\left\{U\subseteq\mathbb{R}-\pi,\pi)\subseteq U\right\}" />? What's wrong? clearly if then and similarly for the intersection. Or, is this ? It's the same.