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Finite complement topology 
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#1
Oct2607, 11:48 PM

P: 776

I need to show if the finite complement topology,T_3, and the topology having all sets (inf,a) = {xx<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. 


#2
Oct2707, 12:09 AM

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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?



#3
Oct2707, 06:17 PM

P: 776

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? 


#4
Oct2707, 06:21 PM

P: 776

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. 


#5
Oct2707, 08:13 PM

P: 776

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


#6
Oct2707, 09:13 PM

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PF Gold
P: 12,270

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



#7
Oct2807, 11:29 PM

P: 776

Hello?



#8
Oct2907, 06:37 AM

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Thanks
PF Gold
P: 39,510

Look at morphism's post!



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