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Math Help - prove that τ is the topology on ℝ

  1. #1
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    prove that τ is the topology on ℝ

    Define τ⊂ P(ℝ) as follows:
    τ={φ}∪{u⊆ℝ:{-π,π}⊆u} .
    prove that τ is a topology on ℝ .
    Last edited by blbl; May 26th 2010 at 07:53 AM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by blbl View Post
    Define τ⊂ P(ℝ) as follows:
    τ={φ}∪{u⊆ℝ:{-π,π}⊆u} .
    prove that τ is the topology on ℝ .
    Is this -\pi,\pi)\subseteq U\right\}" alt="T=\{\varnothing\}\cup\left\{U\subseteq\mathbb{R}-\pi,\pi)\subseteq U\right\}" />? What's wrong? clearly \varnothing,\mathbb{R}\in T if (-\pi,\pi)\subseteq U_\alpha then (-\pi,\pi)\subseteq\bigcup_{\alpha\in\mathcal{A}}U_\  alpha and similarly for the intersection. Or, is this T=\{\varnothing\}\cup\left\{U\subseteq\mathbb{R}:\  {-\pi,\pi\}\subseteq U\right\}? It's the same.
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