separation axiom

May 2010
4
0
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
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
Apr 2005
20,249
7,909
For that matter, what does it mean to intersect a set with a number?