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Topology - Metric Space

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data

    For a metric space (X,d) and a subset E of X, de fine each of the terms:

    (i) the ball B(p,r), where pεX and r > 0
    (ii) p is an interior point of E
    (iii) p is a limit point of E


    2. Relevant equations



    3. The attempt at a solution

    i) Br(p) = {xεX: d(x.p)≤r}


    ii) Br(p) = {xεX: d(x.p)≥r}

    iii) I do not know the answer to this at all.

    I do not know if the first two parts are correct either so I would appreciate any help given.
     
  2. jcsd
  3. Feb 24, 2014 #2

    Dick

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    Science Advisor
    Homework Helper

    i) might be ok, if you mean 'closed ball' and d(x.p) should be d(x,p). But seriously, these are definitions. If you don't know what 'interior' or 'limit point' mean you should look them up. The process of looking them up will give you the definitions.
     
  4. Feb 24, 2014 #3
  5. Feb 25, 2014 #4
    ok thanks guys for the help :)
     
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