[QUOTE]Support f: and A (subset) . Define a subset of the pre-image of the set A by and denoted by
= { }
Prove that = , where denotes the complement of X in .
Prove the is continuous <=> for all open V (subset) , is open in
Pls help
[QUOTE]Support f: and A (subset) . Define a subset of the pre-image of the set A by and denoted by
= { }
Prove that = , where denotes the complement of X in .
Prove the is continuous <=> for all open V (subset) , is open in
Pls help
If you expect to have your posts answered, you must learn to post in symbols? You can use LaTeX tags.
[tex] \left(f^{-1}(A)\right)^c[/tex] gives
We cannot help on things we cannot read.
Hi again ^^
I think here a more metric proof is needed, because of we are in so I prefer to say that:
Let be fixed and let be a positive number, we have that is an open set of , so by hypothesis should be an open set in .
Now we take , which means that and therefore .
On the other hand you'll se that there is a positive number such that (look at the set where lies).
Finally we see continuity of at .