anonymous
  • anonymous
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,
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
well its not clear. similar problem
anonymous
  • anonymous
@zzr0ck3r
anonymous
  • anonymous
\[x_{n}\rightarrow x \epsilon, as, n\rightarrow N \]

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anonymous
  • anonymous
thats option one . which i fink is correct
zzr0ck3r
  • zzr0ck3r
one min
zzr0ck3r
  • zzr0ck3r
please stop using epsilon lol
anonymous
  • anonymous
\[\forall U \in N(x), we have N \in \mathbb N \forall n\geqslant N, x_{n}\epsilon U \] option B
zzr0ck3r
  • 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
anonymous
  • anonymous
ok sir
zzr0ck3r
  • zzr0ck3r
back
anonymous
  • anonymous
@zzr0ck3r
anonymous
  • anonymous
@zzr0ck3r
zzr0ck3r
  • zzr0ck3r
hi
anonymous
  • anonymous
hi sir
anonymous
  • anonymous
anonymous
  • 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
anonymous
  • anonymous
please they are two but help with this sir
zzr0ck3r
  • zzr0ck3r
What does complete mean, and what does dense mean?
zzr0ck3r
  • zzr0ck3r
and what does countable mean?
anonymous
  • anonymous
a countable set is a set with the same cardinality
zzr0ck3r
  • zzr0ck3r
the same carnality as what?
anonymous
  • anonymous
some subset of the set
zzr0ck3r
  • 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

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