Show that the boundary of any set D is itself a closed set.

Thanks in advance for any advice...

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- February 1st 2010, 10:29 PMjzelltProof of Topological Property
Show that the boundary of any set D is itself a closed set.

Thanks in advance for any advice... - February 2nd 2010, 07:31 AMPlato
Suppose that is the boundary of .

If is a limit point of and is and open set such that implies .

That means that because is a boundary point, must contain a point of and a point not in .

How does this prove that is a boundary point of ? How does that show that is closed? - February 3rd 2010, 02:23 PMDrexel28
....sooo...

- February 3rd 2010, 03:18 PMmabruka
Maybe state what definition of boundary you are starting from ?