# Math Help - separation axiom

1. ## separation axiom

Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ}

2. Originally Posted by blbl
Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ}
What does this even mean? What is $T_{\sqrt{2}}=\left\{U\cap\sqrt{2}:U\in T\right\}$?? Are you saying the only open set is $\sqrt{2}$?

3. For that matter, what does it mean to intersect a set with a number?