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

I was thinking of the result that every compact metric space is the continuous image

of the Cantor set/space C. This result is built on some results like the fact that 2nd

countable metric spaces can be embedded in I^n (I is --I am?-- the unit interval),

the fact that there is a continuous map between C and I, and, from what I read

recently , the fact that every closed subset of C is a retract of C.

How do we know that every closed subset of C is a retract of C?

**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!

# Cantor Set/Space and Retracts.

Loading...

Similar Threads - Cantor Space Retracts | Date |
---|---|

I Polarization Formulae for Inner-Product Spaces ... | Mar 9, 2018 |

I Cantor's intersection theorem (Apostol) | Mar 25, 2016 |

Hausdorff dimension of the cantor set | Sep 14, 2013 |

Cantor Set - Perfect and Totally Disconnected | Jan 10, 2013 |

Cantor set | Aug 19, 2012 |

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