Non-Homogeneous Topology: Finding an Example

[latentcorpse]

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.

 

[Hurkyl]

Intuitively I think I'm looking for a space where one part of it has different topological properties from another location.

What difficulty are you having translating this into an example? Just pick the parts and put them into a space.

 

[latentcorpse]

so could i pick say the real line $\mathbb{R}$ as my space but with different metrics in different parts

i.e.

$\forall x \geq 0, d(x,y)=x-y$

$\forall x<0, d(x,y) = x+y$

or something like that?

 

[lanedance]

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