anonymous one year ago Let X be a topological space, Let {x_{n} be a sequence of elements in X. Then x_{n} is said to converge to x\epsilon X if \forall nbds U of x, there existsN\epsilon\mathbb Nsuch that \forall n\geslant N, x_{n}\epsilon U. i.e one of these conditions does not hold x_{n}\rightarrowx\epsilon as n\rightarrow N \forall U\epsilon N(x), we have N\epsilon \epsilon \mathbb N \forall n\geqslantN, x_{n}\epsilon U x_{n}\rightarrowx\epsilon as n\righ = N \forall U\epsilon N(x), we have N\epsilon \epsilon \mathbb N \forall n\geqslantN,

1. anonymous

well its not clear. similar problem

2. anonymous

@zzr0ck3r

3. anonymous

$x_{n}\rightarrow x \epsilon, as, n\rightarrow N$

4. anonymous

thats option one . which i fink is correct

5. zzr0ck3r

one min

6. zzr0ck3r

7. anonymous

$\forall U \in N(x), we have N \in \mathbb N \forall n\geqslant N, x_{n}\epsilon U$ option B

8. zzr0ck3r

I can read this... I will be back in a bit. I have no idea what this means $x_{n}\rightarrow x\epsilon\text{ as } n\rightarrow N$ Please, STOP USING EPSILON, and STOP PUTTING TEXT IN LINE WITH MATH it makes this impossible. bbl

9. anonymous

ok sir

10. zzr0ck3r

back

11. anonymous

@zzr0ck3r

12. anonymous

@zzr0ck3r

13. zzr0ck3r

hi

14. anonymous

hi sir

15. anonymous

16. anonymous

Let X be a complete metric space and {On} is countable collection of dense open subset of X. Show that $\cup O_n$ is not empty

17. anonymous

please they are two but help with this sir

18. zzr0ck3r

What does complete mean, and what does dense mean?

19. zzr0ck3r

and what does countable mean?

20. anonymous

a countable set is a set with the same cardinality

21. zzr0ck3r

the same carnality as what?

22. anonymous

some subset of the set

23. zzr0ck3r

this is not correct(not even close). You are jumping way to far ahead. I am not trying to be rude, but I don't to waste time doing this if you will not understand