Adherent and boundary point

[baldo891]

Studing complex analysis in lang's book i found this "A point $a$ is said to be adherent to S if every disc $D(a,r)$ with r>0 contains some element of S.
how can translate adherent?
Boundary point= punto di confine it is right?
Bounded=limitato it is right?

[baldo891]

thanks

[legendre]

http://mathworld.wolfram.com/BoundaryPoint.html

[dissonance]

@fu: I don't think so. Typically $a$ is said to be a "punto di accumulazione" for a set $S$ iff every neighborhood of $a$ contains some point of $S$ other than $a$. Specifically, even if $a$ belongs to $S$ there is no need for it to be a "punto di accumulazione" for $S$: e.g. if $S={a}$, $a$ is not a "punto di accumulazione" for $S$.
This is different from baldo's definition. In fact every "punto di accumulazione" is an adherent point in baldo's sense that is not a member of the set.

[edit] Wrong. The correct statement is

every "punto di accumulazione" is an adherent point in baldo's sense that is not an isolated point.

[/edit]

A good translation for baldo's "adherent point" would be "punto di aderenza", even if I usually call "chiusura" the set of adherent points:

"... $a$ is adherent to $S$ ... "
becomes
"... $a$ appartiene alla chiusura di $S$ ..."

but it's just a matter of taste.

On the other hand, I've noticed there's no unified notation for the Italian "punto di accumulazione". In fact I have the feeling that the concept itself is less used in English books. Some authors, such as Munkres, call them "limit points" or "accumulation points" but the same notations appear in other books for adherent points.

[gugo82]

"baldo89":Boundary point= punto di confine it is right?

You can translate boundary with "frontiera"; hence boundary point with "punto di frontiera".

"baldo89":Bounded=limitato it is right?

Correct.

[apatriarca]

adherent point = punto di aderenza

[fu^2]

I think that you can "translate" adherent as "di accumulazione."

In fact in italian language I can say " un punto "a" è detto essere di accumulazione per $S$ se ogni disco $D(a,r)$, con $r>0$ contine qualche elemento di $S$.

is it Ok?...