# separation axiom

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• May 25th 2010, 12:25 AM
blbl
separation axiom
Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ}
• May 25th 2010, 12:30 AM
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, 02:37 AM
HallsofIvy
For that matter, what does it mean to intersect a set with a number?