Convergence of sequences in topological spaces?

[~Death~]

hi
I was having difficulty with this problem in the book

If (1/n) is a sequence in R

which points (if any) will it converge (for every open set there is an integer N such that for all n>N 1/n is in that open set) to using the following topologies

(a) Discrete
(b) Indiscrete
(c) { A in X : A\X is countable or all of X }

For indiscrete I know that any sequence will converge to any point in R

For discrete -the sequence doesn't coverge to any points

and for (c) I am thinking the sequence again doesn't converge to any points

but I am not sure how to prove the last ones ...or if theyre even right

any help?

 

[Office_Shredder]

A\X is countable or all of X }

What do you mean by A\X? Most people write set theoretic subtraction as X\A (since A is a subset of X, you can't subtract X from A meaningfully), is that your intent?

 

[~Death~]

What do you mean by A\X? Most people write set theoretic subtraction as X\A (since A is a subset of X, you can't subtract X from A meaningfully), is that your intent?

yea that's what i meant, sorry -)

 

[~Death~]

i don't really require a proof - i just want to know if i got the right answers
that is discrete topology -no point of convergence
indiscrete -all points are points of convergence
and the last one -no point is a point of convergence

thanks

 

[Moo Of Doom]

Yes, those answers are correct to the best of my knowledge.