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The question is to find all the cluster points of set $\{(x,y) | x>0, y>0\}$ in $\mathbb{R}^2$. Just want to confirm my answer. The answer is all the points of 1 st quadrant of $\mathbb{R}^2$ with points on the axes. So, whether i found it correct? How shall I show this formally?

Giovanni
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Kavita
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1 Answers1

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Yes you are right the set of cluster points of your given set is $\{(x,y) \in \mathbb{R}^2 , x \geq 0, y \geq 0 \}$ (i.e. all the points of 1 st quadrant of \mathbb{R}^2 with points on the axes). To prove this formaly you may use the definition used here Definition of cluster point .

Nizar
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