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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,

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  1. anonymous
    • one year ago
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    well its not clear. similar problem

  2. anonymous
    • one year ago
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    @zzr0ck3r

  3. anonymous
    • one year ago
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    \[x_{n}\rightarrow x \epsilon, as, n\rightarrow N \]

  4. anonymous
    • one year ago
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    thats option one . which i fink is correct

  5. zzr0ck3r
    • one year ago
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    one min

  6. zzr0ck3r
    • one year ago
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    please stop using epsilon lol

  7. anonymous
    • one year ago
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    \[\forall U \in N(x), we have N \in \mathbb N \forall n\geqslant N, x_{n}\epsilon U \] option B

  8. zzr0ck3r
    • one year ago
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    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
    • one year ago
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    ok sir

  10. zzr0ck3r
    • one year ago
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    back

  11. anonymous
    • one year ago
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    @zzr0ck3r

  12. anonymous
    • one year ago
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    @zzr0ck3r

  13. zzr0ck3r
    • one year ago
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    hi

  14. anonymous
    • one year ago
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    hi sir

  15. anonymous
    • one year ago
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  16. anonymous
    • one year ago
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    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
    • one year ago
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    please they are two but help with this sir

  18. zzr0ck3r
    • one year ago
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    What does complete mean, and what does dense mean?

  19. zzr0ck3r
    • one year ago
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    and what does countable mean?

  20. anonymous
    • one year ago
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    a countable set is a set with the same cardinality

  21. zzr0ck3r
    • one year ago
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    the same carnality as what?

  22. anonymous
    • one year ago
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    some subset of the set

  23. zzr0ck3r
    • one year ago
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    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

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spraguer (Moderator)
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