1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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)?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Another Topology Question
  1. Topology Question (Replies: 4)

  2. Topology question (Replies: 2)

  3. Topology question (Replies: 5)