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Homework Help: Another Topology Question

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data
    If L is a straight line in the plane, describe the topology L inherits
    as a subspace of RlxR and as a subspace of RlxRl in each case it is a
    familiar topology.(Rl= lower limit topology)

    3. The attempt at a solution

    RlxR topology is the union of intervals [a,b)x(c,d) which is any open interval in R^2. Likewise for the topology of RlxRl. Hence any intersection between open intervals in R^2 and the line y=mx+b will be an open interval of the line. So in both cases, won't the inherited topology just be R?
  2. jcsd
  3. Nov 20, 2007 #2


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    Science Advisor
    Homework Helper

    It won't always be the inherited topology from R. For example in R_l x R, take the line y=-x (i.e. the set {(x,-x)}). What happens when you intersect it with the square [a,b)x(c,d)?
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