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Set Point Topology-product and connected spaces.

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data

    1. Prove that the space C([0,1]) is arc-connected (C([0,1]) = real continous functions onto [0,1] with the metric max|f(x)-g(x)| )

    2. Prove that in a product space of infinite many spaces, such as in each space there is more than one point, every point is an accumulation point.

    3. Prove that [tex] R_{CF} [/tex] is path-connected but not arc-connected.

    2. Relevant equations
    3. The attempt at a solution
    I'm realy bad at all the path-connected&arc-connected subject so I can't realy understand how I should start solving these 3 problems...I have no clue about them...


    Tnx in advance
     
  2. jcsd
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