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

Thank you!

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- Mar 30th 2011, 04:24 PMConnectedLooking the name
If $\displaystyle x\in A$ verifies that $\displaystyle \forall\epsilon:B(x,\epsilon)\cap A\ne\varnothing,$ how is it called?

Thank you! - Mar 30th 2011, 04:48 PMbkarpuz
- Mar 30th 2011, 04:54 PMConnected
No, no typo, it's just that I want to know how the point $\displaystyle x$ is called.

- Mar 30th 2011, 04:58 PMbkarpuz
- Mar 30th 2011, 05:02 PMConnected
Haha, okay, perhaps another known example:

$\displaystyle x\in A$ is said to be an interior point of $\displaystyle A$ if $\displaystyle \exists\delta>0:B(x,\delta)\subseteq A.$ - Mar 30th 2011, 05:08 PMbkarpuz
$\displaystyle x\in X$ is said to be an accumulation (limit) point of $\displaystyle A$

provided that $\displaystyle (B(x,\varepsilon)\backslash\{x\})\cap A\neq\emptyset$ for every $\displaystyle \varepsilon>0$.

May be you are looking for this one? - Mar 30th 2011, 05:13 PMConnected
Got it, the concept is "adherent point."

- Mar 30th 2011, 05:14 PMDrexel28
- Mar 30th 2011, 05:18 PMConnected
I think the other name that has is "closure point," does that make sense?