Is infinity part of the boundary of R^n?

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I am having a set $S= xin(-1,1), yin(0,infty) $. Does $bar S$S include the set of points for which $ytoinfty$; figuratively speaking, does it include the "boundary" at infinity?



Thanks for explanations!






general-topology infinity







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    Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
    – Lord Shark the Unknown
    Sep 2 at 10:59











  • As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
    – Yanko
    Sep 2 at 11:12














up vote
0
down vote

favorite












I am having a set $S= xin(-1,1), yin(0,infty) $. Does $bar S$S include the set of points for which $ytoinfty$; figuratively speaking, does it include the "boundary" at infinity?



Thanks for explanations!






general-topology infinity







share|cite|improve this question

















  • 2




    Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
    – Lord Shark the Unknown
    Sep 2 at 10:59











  • As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
    – Yanko
    Sep 2 at 11:12












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I am having a set $S= xin(-1,1), yin(0,infty) $. Does $bar S$S include the set of points for which $ytoinfty$; figuratively speaking, does it include the "boundary" at infinity?



Thanks for explanations!






general-topology infinity







share|cite|improve this question













I am having a set $S= xin(-1,1), yin(0,infty) $. Does $bar S$S include the set of points for which $ytoinfty$; figuratively speaking, does it include the "boundary" at infinity?



Thanks for explanations!






general-topology infinity




general-topology infinity






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asked Sep 2 at 10:57









Britzel

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31







  • 2




    Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
    – Lord Shark the Unknown
    Sep 2 at 10:59











  • As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
    – Yanko
    Sep 2 at 11:12












  • 2




    Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
    – Lord Shark the Unknown
    Sep 2 at 10:59











  • As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
    – Yanko
    Sep 2 at 11:12







2




2




Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
– Lord Shark the Unknown
Sep 2 at 10:59





Talking about a closure $overline S$ presupposes an ambient topological space in which the closure is taken. If this space is $Bbb R^2$, then the answer is "no".
– Lord Shark the Unknown
Sep 2 at 10:59













As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
– Yanko
Sep 2 at 11:12




As an easier example you may consider $(0,infty)subseteqmathbbR$ the closure of this set does not contain infinity simply because $inftynotinmathbbR$.
– Yanko
Sep 2 at 11:12










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Normally it doesn't. The overall space you are considering does not contain infinity either as a point itself. Normally for you to have infinity you would do a one point compactification of your space, very similar to the extended complex plane.






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    accepted










    Normally it doesn't. The overall space you are considering does not contain infinity either as a point itself. Normally for you to have infinity you would do a one point compactification of your space, very similar to the extended complex plane.






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      down vote



      accepted










      Normally it doesn't. The overall space you are considering does not contain infinity either as a point itself. Normally for you to have infinity you would do a one point compactification of your space, very similar to the extended complex plane.






      share|cite|improve this answer






















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        Normally it doesn't. The overall space you are considering does not contain infinity either as a point itself. Normally for you to have infinity you would do a one point compactification of your space, very similar to the extended complex plane.






        share|cite|improve this answer












        Normally it doesn't. The overall space you are considering does not contain infinity either as a point itself. Normally for you to have infinity you would do a one point compactification of your space, very similar to the extended complex plane.







        share|cite|improve this answer












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        answered Sep 2 at 11:01









        Fundamentals

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