Have a look at the web reference
Note that is the boundary of A which is a closed set so that
Dear Colleagues,
I want a help for proving the following property:
Bd[Bd{Bd(A)}]=Bd[Bd(A)], where Bd denotes the boundary and A is subset of a toplogical space X.
Actually I proved that Bd[Bd{Bd(A)}] is a subset of Bd[Bd(A)] but I could not prove the converse.
Regards,
Raed.
Have a look at the web reference
Note that is the boundary of A which is a closed set so that
Well I have not have any idea what to tell you.
It is clear on that webpage I gave you.
It says "For any set S, ∂S ⊇ ∂∂S, with equality holding if and only if the boundary of S has no interior points, which will be the case for example if S is either closed or open. Since the boundary of a set is closed, ∂∂S = ∂∂∂S for any set S.
If is a set then the closure .
Thus if is closed.
Is it possible that has any interior points?