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Math Help - Looking the name

  1. #1
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    Looking the name

    If x\in A verifies that \forall\epsilon:B(x,\epsilon)\cap A\ne\varnothing, how is it called?

    Thank you!
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  2. #2
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by Connected View Post
    If x\in A verifies that \forall\epsilon:B(x,\epsilon)\cap A\ne\varnothing, how is it called?
    Is there a typo here?
    Because this is always true since x\in B(x,\epsilon)\cap A.
    Last edited by bkarpuz; March 30th 2011 at 05:09 PM.
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  3. #3
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    No, no typo, it's just that I want to know how the point x is called.
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  4. #4
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by Connected View Post
    No, no typo, it's just that I want to know how the point x is called.
    Then I want to learn this too.
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  5. #5
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    Haha, okay, perhaps another known example:

    x\in A is said to be an interior point of A if \exists\delta>0:B(x,\delta)\subseteq A.
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  6. #6
    Senior Member bkarpuz's Avatar
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    x\in X is said to be an accumulation (limit) point of A
    provided that (B(x,\varepsilon)\backslash\{x\})\cap A\neq\emptyset for every \varepsilon>0.

    May be you are looking for this one?
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  7. #7
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    Got it, the concept is "adherent point."
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  8. #8
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Connected View Post
    Got it, the concept is "adherent point."
    What you mean to say is that x\in A or etc.
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  9. #9
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    I think the other name that has is "closure point," does that make sense?
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