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Closed and open subsets

  1. Oct 31, 2012 #1
    1. {(x,y)[itex]\in[/itex] R^2 such that 2x+y<=2, x-y>4} Determine whether this subset of R^2 is open, closed or neither open nor closed.


    2. I think this is an open subset but not sure how to prove it. I have rearranged the equations to give x>2, y<=-2x+1, y< x-1. I think it is open because x can get closer and closer to 2 but never equal it and y can get closer and closer to x-1 but never equal it. I'm not sure how prove this mathematically though?

    Any help or hints would be great!
     
  2. jcsd
  3. Oct 31, 2012 #2

    Zondrina

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    Homework Helper

    First things first. Draw what your set looks like by re-arranging your equations a bit. This will allow you to see whether or not your set is open.

    Remember a set is open if every point is an interior point, that is for any point you choose, every neighborhood around it contains points only from the set.
     
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