Question

help here

Answer 1

yes

Answer 2

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 exists N\[\epsilon \] N such that \[\forall \] n\[\geslant \] N, \[x_{n} \]\[\epsilon \] U

Answer 3

then one of these conditions does not hold

Answer 4

A) \[x_{n} \rightarrow x , as.. n\rightarrow N \]

Answer 5

ya this is not in my range of knowledge, that looks like 20 years of college

Answer 6

The option you showed is true.