# Homework Help: Finite complement topology

1. Oct 26, 2007

### Nusc

I need to show if the finite complement topology,T_3, and the topology having all sets (-inf,a) = {x|x<a} as basis ,T_5, are comparable.

I've shown that T_3 is not strictly finer than T_5.

But I'm not sure about other case.

I need help.

Last edited by a moderator: Mar 8, 2013
2. Oct 27, 2007

### morphism

I presume you're defining these topologies on R and that you managed to find a set in T_5 that's not in T_3. The other direction is just as easy: is R\{0} in T_5?

3. Oct 27, 2007

### Nusc

R\{0} is not in T_5. (-inf,0]U[0,inf)

If T_4 is the upper limit topology, having the sets (a,b] as a basis and
T_2 the topology of R_K (a,b)-K K = 1/n n in Z.

I've shown that T_2 is not strictly finer than T_4.
How do I show that T_4 is strictly finer than T_2?

Last edited: Oct 27, 2007
4. Oct 27, 2007

### Nusc

And most importantly, why is R\{1,2,3} considered a basis element for T_3?

It's not finite, nor is it all of R. I'm confused with the definition of a finite complement topology.

5. Oct 27, 2007

### Nusc

Topology

Is {1} = (0,2) ?
and R\{0} = (-inf,0]U[0,inf) ?

Last edited: Oct 27, 2007
6. Oct 27, 2007

### Moonbear

Staff Emeritus
Note: I have merged your two threads on this since you had already received responses in the Calc and Analysis forum.

7. Oct 28, 2007

### Nusc

Hello?

8. Oct 29, 2007

### HallsofIvy

Look at morphism's post!