# Topology Question

1. Nov 16, 2009

### 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.

2. Nov 16, 2009

### Hurkyl

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

3. Nov 16, 2009

### 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?

4. Nov 16, 2009

### lanedance

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