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

yes

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

yes it is like that

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

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

But discrete points are itself closed set.

where does this problem come from (book) ??

assignment

which book are you using as Text Book ??

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

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

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

i understand it this way but i can't show it |dw:1361566625628:dw|

|dw:1361567087644:dw|

is X compact??

"compact "what do u mean

X-{x}

is what i am thinking "but not quit sure"

let me ask experts ... I'll reply you in sometime.

i think since the subset of X are open this also implies that {x}and its complements are also open

i got the hint: in the discret topology all points are open

so does this mean that there is no relationship between {x} and its complement

no ... use the fact that union of infinite number of open sets is and open set.

or simply just union of open sets.

i mean like "ie if {x} is open it does not imply that its complement is also closed "

is it possible ?

I guess not in discrete topology

|dw:1361569963336:dw|
usually we have neither closed nor open set.

ok i get ur statement

P.S. I am not sure, I don't have experience with Topology.

I am an engineer, and have not studied analysis.

|dw:1361653147330:dw|
i think they mean it this way because of the question