I have a set i.e the diagonal of the unit square. How to show that A is closed??

By definition a set is closed if it's complement is open, so I need to show that is an open set. What will be in this case?

?

is ?

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- September 23rd 2013, 04:09 AMraymanshow that a set is closed
I have a set i.e the diagonal of the unit square. How to show that A is closed??

By definition a set is closed if it's complement is open, so I need to show that is an open set. What will be in this case?

?

is ? - September 23rd 2013, 04:42 AMPlatoRe: show that a set is closed
- September 23rd 2013, 05:39 AMraymanRe: show that a set is closed
thank you for the help. I have a question.

Just to clarify

is the radius of the open ball ? (from the formula I get in the denominator)

What about the end points of A? Don't we have to find open balls in the neighborhood of these two with the proper radius? - September 23rd 2013, 06:54 AMPlatoRe: show that a set is closed
I used because that makes the closure of the ball disjoint from .

That is merely a matter of choice.

I don't know what you mean by "What about the end points of A?"

The proof I gave is in fact the way we show that anyin is a closed set.*line* - September 23rd 2013, 07:04 AMraymanRe: show that a set is closed
Thanks again for helping.