Finding a sequence of sets whose limit is a given set











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Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?






real-analysis measure-theory elementary-set-theory







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    Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
    – Lord Shark the Unknown
    10 hours ago










  • $F$ is a part of $B$ and so their intersection is not empty.
    – M. Rahmat
    9 hours ago















up vote
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Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?






real-analysis measure-theory elementary-set-theory







share|cite|improve this question


















  • 2




    Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
    – Lord Shark the Unknown
    10 hours ago










  • $F$ is a part of $B$ and so their intersection is not empty.
    – M. Rahmat
    9 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?






real-analysis measure-theory elementary-set-theory







share|cite|improve this question













Suppose $B$ is a ball in $mathbb{R}^{n}$ with $n>1$, and $F$ a closed set with empty interior. Is there an increasing sequence of sets $E_{1}subset,...E_{n}subset E_{n+1},...$, all Borel sets, such that each $E_{n}subset Bsetminus F$ but $cup_{n}E_{n}=B$?






real-analysis measure-theory elementary-set-theory




real-analysis measure-theory elementary-set-theory






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 10 hours ago









M. Rahmat

292211




292211








  • 2




    Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
    – Lord Shark the Unknown
    10 hours ago










  • $F$ is a part of $B$ and so their intersection is not empty.
    – M. Rahmat
    9 hours ago














  • 2




    Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
    – Lord Shark the Unknown
    10 hours ago










  • $F$ is a part of $B$ and so their intersection is not empty.
    – M. Rahmat
    9 hours ago








2




2




Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago




Not if $Bcap F$ is nonempty. Is this actually the question you wished to ask?
– Lord Shark the Unknown
10 hours ago












$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago




$F$ is a part of $B$ and so their intersection is not empty.
– M. Rahmat
9 hours ago















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