# separation axiom

#### blbl

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

#### Drexel28

MHF Hall of Honor
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 $$\displaystyle T_{\sqrt{2}}=\left\{U\cap\sqrt{2}:U\in T\right\}$$?? Are you saying the only open set is $$\displaystyle \sqrt{2}$$?

#### HallsofIvy

MHF Helper
For that matter, what does it mean to intersect a set with a number?