Looking the name

**Connected** · March 30th 2011, 04:24 PM

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

Thank you!

**bkarpuz** · March 30th 2011, 04:48 PM

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 $x\in B(x,\epsilon)\cap A$ .

**Connected** · March 30th 2011, 04:54 PM

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

**bkarpuz** · March 30th 2011, 04:58 PM

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.

**Connected** · March 30th 2011, 05:02 PM

Haha, okay, perhaps another known example:

$x\in A$ is said to be an interior point of $A$ if $\exists\delta>0:B(x,\delta)\subseteq A.$

**bkarpuz** · March 30th 2011, 05:08 PM

$x\in X$ 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?

**Connected** · March 30th 2011, 05:13 PM

Got it, the concept is "adherent point."

**Drexel28** · March 30th 2011, 05:14 PM

Originally Posted by Connected

Got it, the concept is "adherent point."

What you mean to say is that $x\in A$ or etc.

**Connected** · March 30th 2011, 05:18 PM

I think the other name that has is "closure point," does that make sense?

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Looking the name