Interior of a subset of $mathbb{R}^3$ where $(x,y)inmathbb{Q}^2$












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I'm having problems to visualize the interior and accumulation points of this set $$
D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
$$



I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?






general-topology multivariable-calculus







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    0












    $begingroup$


    I'm having problems to visualize the interior and accumulation points of this set $$
    D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
    $$



    I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?






    general-topology multivariable-calculus







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I'm having problems to visualize the interior and accumulation points of this set $$
      D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
      $$



      I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?






      general-topology multivariable-calculus







      share|cite|improve this question









      $endgroup$




      I'm having problems to visualize the interior and accumulation points of this set $$
      D = left{ (x,y,z)inmathbb{R}^3 ; : ; z = 5-x^2-y^2 geq 0, (x,y) in mathbb{Q}timesmathbb{Q}right}cup left{left(4,4,frac{1}{n}right) ; : ; nin mathbb{N} right}
      $$



      I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{mathrm{o}}$ empty?






      general-topology multivariable-calculus




      general-topology multivariable-calculus






      share|cite|improve this question













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      asked Jan 18 at 8:54









      Raúl AsteteRaúl Astete

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          $begingroup$

          The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).






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            1 Answer
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            active

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            2












            $begingroup$

            The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).






            share|cite|improve this answer









            $endgroup$


















              2












              $begingroup$

              The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).






              share|cite|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).






                share|cite|improve this answer









                $endgroup$



                The set $mathring D$ is empty, since $D$ is countable (which follows from the fact that $mathbb Q$ is countable).







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 18 at 8:56









                José Carlos SantosJosé Carlos Santos

                164k22131234




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