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Math Help - Topology: product, uniform, and box topology converging sequences

  1. #1
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    Topology: product, uniform, and box topology converging sequences

    I'm having a lot of trouble understanding how to work a problem like this from topology...

    Consider the product, uniform, and box topologies on Rw (that's an omega)
    In which topologies do the following sequences converge?
    w1 = (1,1,1,1,...)
    w2 = (0,2,2,2,...)
    w3 = (0,0,3,3,...)
    ...
    x1 = (1,1,1,1,...)
    x2 = (0,1/2,1/2,1/2,...)
    x3 = (0,0,1/3,1/3,...)
    ...
    y1 = (1,0,0,0,...)
    y2 = (1/2,1/2,0,0,...)
    y3 = (1/3,1/3,1/3,0...)
    ...
    z1 = (1,1,0,0,...)
    z2 = (1/2,1/2,0,0,...)
    z3 = (1/3,1/3,0,0...)
    ...

    Any help would be great...even just one set of the variables so I could have an example of where to go...Thanks!
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  2. #2
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    Re: Topology: product, uniform, and box topology converging sequences

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