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analysis question

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  • Casey
    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
    • Noel Vaillant
      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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