What definition of "base" for a topology are you using?
Hi there
Prove this statement or the opposite:
Consider the set . Define .
The collection is a base for a topology on .
Is this true or not? Why? I'm sorry but I don't understand a lot after reading this multiple times?? How do I show that it is a base of a topology and which one?
Could maybe please someone give me a hint?
Regards
Thank you.
So I have to differ between the disjoint and the non-disjoint case, don't I ?
disjoint case:
For r=0 U(0)= and so it is true that .
Hmm, I am not convinced of this argument because one could always head this statement for S, T arbitrary. There was always ?
non-disjoint case:
Then
fullfills the condition above.
So since ??
So since ??
What about the other parameters used by "min". They make sure that the whole Ball is contained in . How can I show formally that they are needed and make sure that the statement is true?
So the topology is
Obviously the family of balls
where covers
What do you think?
Regards