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What is the closure of the set $\left\{\left(x,y\right)\in \mathbb{R}^2:x^2+y^2> 1\right\}$?

  • 4
    What are your thoughts on the problem? Any guesses? Do you have to prove your answer? – 2017-02-12
  • 2
    Can you say what's the definition of closure? – 2017-02-12

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The logical answer is $\{(x, y) \in \mathbb{R}^{2} | x^2 + y^2 \geq 1\},$ isn't it? Let's try to prove that. We know that if $A$ is a set, $\overline{A},$ the closure of that set, is equal to $A \space \cup \space A' ,$ where $A'$ denotes the set of limit points of $A$. Can you find $A'$?