# Thread: How to determine if a point is a closure point of a set

1. ## How to determine if a point is a closure point of a set

How to determine if for e.g. (3,0) is a closure point of a set C
where C=A ∩ B
Where A=1
x^2+y^2≤9
B=IxI>1

How would I start something like this?

2. ## Re: How to determine if a point is a closure point of a set

A point, P, is a closure point of set S (is in the closure of S) if and only if every open neighborhood of P contains a point of X. Here, (3, 0) is in set B and $3^2+ 0^2= 9$ so, for any $\epsilon> 0$, $(3- \epsilon, 0)$ is in C.

3. ## Re: How to determine if a point is a closure point of a set Originally Posted by asrm How to determine if for e.g. (3,0) is a closure point of a set C
where C=A ∩ B
Where A=1≤x^2+y^2≤9
B=IxI>1 How would I start something like this?
Denote the closure of $X$ by $\overline{X}$
Using that definition it is clear that $X\subseteq\overline{X}$. In this case is it true that $(3,0)\in A\cap B~?$

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