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Math Help - Topology Proof

  1. #1
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    Topology Proof

    Prove: For any topologies T1 and T2 for X, if B1 is a base for T1, and if B1 ⊂ T2, then T1 ⊂ T2.

    Using:
    Thm 2.1: A is open in (X,T) iff For every p ∈ A, there is G ∈T such that p ∈ G and G ⊂ A
    Cor 8.2: B is a base for T iff: B ⊂ T and for every G ∈ T, if p ∈G, then there is A ∈ B such that p is an element of A ⊂ G


    Last edited by Kiefer; September 27th 2012 at 12:43 PM.
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  2. #2
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    Re: Topology Proof

    Quote Originally Posted by Kiefer View Post
    Prove: For any topologies T1 and T2 for X, if B1 is a base for T1, and if B1 is a subset of T1, then T1 is a subset of T2.
    Please review your posting. I think that you have a misplaced subscript.
    Do you mean B_1\subset T_2~?
    Thanks from Kiefer
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  3. #3
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    Re: Topology Proof

    Quote Originally Posted by Kiefer View Post
    Prove: For any topologies T1 and T2 for X, if B1 is a base for T1, and if B1 ⊂ T2, then T1 ⊂ T2.
    Thank you for the edit.
    If O\in T_1 then then is a collection of sets B_{\alpha} from B such that O = \bigcup\limits_\alpha  {B_\alpha  } (basis)

    Because T_2 is a topology and B\subset T_2 we know that O = \bigcup\limits_\alpha  {B_\alpha  }  \in T_2 .

    Proof done.
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  4. #4
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    Re: Topology Proof

    can somebody help me with these two problems immediately???


    1.Let D_p be any open disc in RR with centre p=(a,b) and radius δ>0.Show that there exist an open disc (Dbar) such that
    (i)the centre of (Dbar) has rational coordinates.
    (ii) the radius of (Dbar0 is rational.
    (iii)p is an element of (Dbar) and (Dbar) is a subdet of D_p


    2.Let f:R→R be a continuous function such that f(q)=sin⁡q for q∈Q.Find the value of f(π/4).
    Last edited by chath; October 16th 2012 at 07:18 AM.
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    Re: Topology Proof

    Please post new questions in new threads.

    -Dan
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