Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I would like to understand why a circle (and in general a n-sphere) as a subset of R^2 (in general R^(n+1)) with the standard topolgy is considered a closed and a bounded set.

I think that this can be a closed set because its complement (the interior of the circle and the rest of the plane) is open. And could be bounded because it has a finite extension (but ths is very intuitive). I cannot figure out what is the interior, the closure or the boundary of this set.

Thank you for your help.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The circle as a set closed and bounded

Loading...

Similar Threads for circle closed bounded | Date |
---|---|

I Turning the square into a circle | Feb 16, 2018 |

I Impossible to lift the identity map on the circle | Oct 10, 2017 |

I Proof that retract of Hausdorff space is closed | Oct 8, 2017 |

I Why is this line not homeomorphic to the unit circle? | Sep 13, 2017 |

I Is the circle a manifold? | Jun 9, 2017 |

**Physics Forums - The Fusion of Science and Community**