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Math Help - separation axiom

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    separation axiom

    Prove that (ℝ,τ_{√2})is T₀ but not T₁,T₂, , Regular , normal , where τ_{√2}={u∩√2:u∈τ}
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by blbl View Post
    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}?
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    For that matter, what does it mean to intersect a set with a number?
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