## analysis question

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• if A and B are open and A is a subset of B, is it true that: A _union_ boundary(A) is also a subset of B? Thank you very much. Casey
Message 1 of 2 , Aug 6, 2004
if A and B are open and A is a subset of B, is it true that:
A _union_ boundary(A) is also a subset of B?

Thank you very much.
Casey
• Hi Casey, I apologise for the late response (was on holiday :-) If E is a topological space and A
Message 2 of 2 , Aug 14, 2004
Hi Casey,

I apologise for the late response (was on holiday :-)

If E is a topological space and A<=B<=E, A and B are open
in E, and D(A) denotes the boundary of A in E, then
there is no reason why A\/D(A) should be a subset of B.

Take E=R, A=B=]0,1[ then D(A)={0}\/{1}

Now if by D(A) you mean the boundary of A in B, then
of course A\/D(A)<=B (no need for A to be open in B or in E)

Noel.

--- In probability@yahoogroups.com, "Casey" <ychanf3h@y...> wrote:
> if A and B are open and A is a subset of B, is it true that:
> A _union_ boundary(A) is also a subset of B?
>
> Thank you very much.
> Casey
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