B blbl May 2010 4 0 May 25, 2010 #1 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 Nov 2009 4,563 1,566 Berkeley, California May 25, 2010 #2 blbl said: Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ} Click to expand... 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 \(\displaystyle \sqrt{2}\)?

blbl said: Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ} Click to expand... 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 \(\displaystyle \sqrt{2}\)?

H HallsofIvy MHF Helper Apr 2005 20,249 7,909 May 25, 2010 #3 For that matter, what does it mean to intersect a set with a number?