# separation axiom

• May 24th 2010, 11:25 PM
blbl
separation axiom
Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ}
• May 24th 2010, 11:30 PM
Drexel28
Quote:

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 $\sqrt{2}$?
• May 25th 2010, 01:37 AM
HallsofIvy
For that matter, what does it mean to intersect a set with a number?