Re: Topology with open and bd(A).

mina_world a écrit :
Hello sir~

A : open <=> A /\ bd(A) = empty.
(/\ : intersection)

-------------------------------------
(=>)
Since A is open, int A = A.
so, A /\ bd(A) = int A /\ bd(A) = empty.

(<=)
I don't know well.
so, I need your advice.


Recall the definition : bd A= A bar - int(A). So if A /\bd A is empty, it means that no points of A are in A bar- int(A), but every point of A is in A bar, so no points of A are not in int (A), sop A is open.
.

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