Register to reply

Finite complement topology

by Nusc
Tags: complement, finite, topology
Share this thread:
Oct26-07, 11:48 PM
P: 779
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.
Phys.Org News Partner Science news on
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice
Oct27-07, 12:09 AM
Sci Advisor
HW Helper
P: 2,020
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?
Oct27-07, 06:17 PM
P: 779
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?

Oct27-07, 06:21 PM
P: 779
Finite complement topology

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.
Oct27-07, 08:13 PM
P: 779
Is {1} = (0,2) ?
and R\{0} = (-inf,0]U[0,inf) ?
Oct27-07, 09:13 PM
Sci Advisor
PF Gold
Moonbear's Avatar
P: 12,271
Note: I have merged your two threads on this since you had already received responses in the Calc and Analysis forum.
Oct28-07, 11:29 PM
P: 779
Oct29-07, 06:37 AM
Sci Advisor
PF Gold
P: 39,353
Look at morphism's post!

Register to reply

Related Discussions
K topology strictly finer than standard topology Calculus & Beyond Homework 5
Uses of topology General Math 2
Topology help Set Theory, Logic, Probability, Statistics 7
Geometric Topology Vs. Algebraic Topology. General Math 1
Topology and algebraic topology? General Math 3