Looking the name

• Mar 30th 2011, 05:24 PM
Connected
Looking the name
If $x\in A$ verifies that $\forall\epsilon:B(x,\epsilon)\cap A\ne\varnothing,$ how is it called?

Thank you!
• Mar 30th 2011, 05:48 PM
bkarpuz
Quote:

Originally Posted by Connected
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 $x\in B(x,\epsilon)\cap A$.
• Mar 30th 2011, 05:54 PM
Connected
No, no typo, it's just that I want to know how the point $x$ is called.
• Mar 30th 2011, 05:58 PM
bkarpuz
Quote:

Originally Posted by Connected
No, no typo, it's just that I want to know how the point $x$ is called.

Then I want to learn this too. :)
• Mar 30th 2011, 06:02 PM
Connected
Haha, okay, perhaps another known example:

$x\in A$ is said to be an interior point of $A$ if $\exists\delta>0:B(x,\delta)\subseteq A.$
• Mar 30th 2011, 06:08 PM
bkarpuz
$x\in X$ 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?
• Mar 30th 2011, 06:13 PM
Connected
Got it, the concept is "adherent point."
• Mar 30th 2011, 06:14 PM
Drexel28
Quote:

Originally Posted by Connected
Got it, the concept is "adherent point."

What you mean to say is that $x\in A$ or etc.
• Mar 30th 2011, 06:18 PM
Connected
I think the other name that has is "closure point," does that make sense?