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Math Help - Vocabulary Thread

  1. #1
    MHF Contributor Mathstud28's Avatar
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    Vocabulary Thread

    I started this thread to post questions about words...not math :P.

    I understand what this means \pi_j:A\times B\longmapsto B but they call it a projection map. Is there something else that goes along with \pi_j:A\times B\longmapsto B than meets the eyes?
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    I'm not sure I understand what you're asking for... Are you wondering if there is an application of this ?

    I can show you one (the first that came in my mind), but it has to do with measure theory (product sigma-algebra). So if you're interested, I can show it...
    And Opalg once used them to explain stuff in product topology.


    There another way of seeing these functions, it's calling them the coordinates mappings :
    \pi_1 ~:~ A \times B \to A (note that it's \to and not \mapsto, I don't know how you learnt it, but my teachers always used the second one for defining the function)

    (x_1,x_2) \mapsto x_1


    \pi_2 ~:~ A \times B \to B
    (x_1,x_2) \mapsto x_2
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    I'm not sure I understand what you're asking for... Are you wondering if there is an application of this ?

    I can show you one (the first that came in my mind), but it has to do with measure theory (product sigma-algebra). So if you're interested, I can show it...
    And Opalg once used them to explain stuff in product topology.


    There another way of seeing these functions, it's calling them the coordinates mappings :
    \pi_1 ~:~ A \times B \to A (note that it's \to and not \mapsto, I don't know how you learnt it, but my teachers always used the second one for defining the function)

    (x_1,x_2) \mapsto x_1


    \pi_2 ~:~ A \times B \to B
    (x_1,x_2) \mapsto x_2
    Thank you very much Moo, I found what they meant and it is as I suspected and you of course identified...it was meant to be a coordinate mapping...btw they do use \pi_1:A\times B{\color{red}\longmapsto}B
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