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Topology Question

  1. Nov 16, 2009 #1
    I'm asked to find an example of a non-homogeneous topological space. To be honest I'm not really sure where to get started. Intuitively I think I'm looking for a space where one part of it has different topological properties from another location. I just can't think of a well-known space for which this would be true.
  2. jcsd
  3. Nov 16, 2009 #2


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    What difficulty are you having translating this into an example? Just pick the parts and put them into a space.
  4. Nov 16, 2009 #3
    so could i pick say the real line [itex]\mathbb{R}[/itex] as my space but with different metrics in different parts


    [itex]\forall x \geq 0, d(x,y)=x-y[/itex]

    [itex]\forall x<0, d(x,y) = x+y[/itex]

    or something like that?
  5. Nov 16, 2009 #4


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    i don't know about the non-homogenous topological space part, but i don't think that's a metric
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