General topology: Prove a Set is Open

In summary: Any topology must be given either by specifying a set of open sets - which are simply specified, not proven - or it is constructed from other topologies, as in product or box topologies. I'm guessing you haven't dealt with the latter yet, so you must have been given a specified collection of open sets to start with. What is that...?If you can assume that an open ball is open and that the intersection of two open sets is open, then the proof should be easy. But, showing that an open ball is open would seem to me to be not much different from showing that the set you have is open.The proof is easy if you have an open ball as the original
  • #36
lep11 said:
What's wrong?

Come on! If you take a positive number away what you have gets smaller.
 
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  • #37
PeroK said:
Come on! If you take a positive number away what you have gets smaller.
Okay, true.

I might just give up. I am not smart enough to study crap like this.
 
  • #38
lep11 said:
Okay, true.

I might just give up. I am not smart enough to study crap like this.
I took a break and tried again.

##d(0,z)≥d(0,x)-d(x,z)≥r+1-d(x,z)>r+1-r=1##
 
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Likes PeroK
  • #39
Thank You PeroK!
 
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