Question

Show that {x} are open sets in X for all points x∈X, then all subsets of X are also open in X.

Answer 1

{x} collection of open sets ... open covering of X?

Answer 2

yes

Answer 3

looks like i am not understanding the Q ... you sure the Q is right?

Answer 4

yes it is like that

Answer 5

any background on the Q? for some reason I find point set topology very hard.

Answer 6

what i know that the set is open when all its point are interior

Answer 7

But discrete points are itself closed set.

Answer 8

where does this problem come from (book) ??

Answer 9

assignment

Answer 10

which book are you using as Text Book ??

Answer 11

RG Bartle and DR Sherbert ,introduction to real analysis john wiley &sons

Answer 12

@walters have you managed to go all though chapters to reach Point Set Topology at the end?

Answer 13

not really but i think his question is open and closed sets

Answer 14

i understand it this way but i can't show it