Question

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,

Answer 1

well its not clear. similar problem

Answer 2

@zzr0ck3r

Answer 3

\[x_{n}\rightarrow x \epsilon, as, n\rightarrow N \]

Answer 4

thats option one . which i fink is correct

Answer 5

one min

Answer 6

please stop using epsilon lol

Answer 7

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

Answer 8

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

Answer 9

ok sir

Answer 10

back

Answer 11

@zzr0ck3r

Answer 12

@zzr0ck3r

Answer 13

hi

Answer 14

hi sir

Answer 15

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

Answer 16

please they are two but help with this sir

Answer 17

What does complete mean, and what does dense mean?

Answer 18

and what does countable mean?

Answer 19

a countable set is a set with the same cardinality

Answer 20

the same carnality as what?

Answer 21

some subset of the set

Answer 22

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