Let M be a connected manifold. Let E be a submanifold of M of codimension at least 2.(adsbygoogle = window.adsbygoogle || []).push({});

Show M\E is connected.

I know examples of this result but how can one generally prove it?

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

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

# Why does removing a submanifold of codim 2 preserve connectivity?

Loading...

Similar Threads - does removing submanifold | Date |
---|---|

I Does a covariant version of Euler-Lagrange exist? | Feb 20, 2018 |

How does regularity of curves prevent "cusps"? | Feb 16, 2015 |

Does spherical symmetry imply spherical submanifolds? | Jun 4, 2014 |

How does metric give complete information about its space? | Apr 15, 2014 |

Fundamental Group of the projective plane after we remove n points? | Oct 29, 2009 |

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