My professor recently defined immersions and embeddings in class, but he didn't really make any attempt to motivate these definitions. Now a few weeks later, after we've been using these concepts in class I'm still having trouble understanding what is *natural* about these definitions, what they *really mean* is still murky... I wonder if there's anyone here who can help me motivate these definitions?(adsbygoogle = window.adsbygoogle || []).push({});

Here's the actual definitions used:

Immersion: a function f from one manifold M to another N is an immersion if it's differential df_p, mapping from a tangent space T_pM to T_f(p)N is injective.

Embedding: An immersion is an embedding if it is 1-1 and it's inverse is continuous.

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

Dismiss Notice

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!

# Immersions and embeddings

Loading...

Similar Threads - Immersions embeddings | Date |
---|---|

I Can there be a bounded space w/o a boundary w/o embedding? | Jul 19, 2016 |

Why are Lie Subgroups Defined as Immersed Submanifolds? | Mar 26, 2014 |

Submanifolds vs Manifolds / Immersion vs Charts | Sep 18, 2012 |

Isometric Immersion of the Torus | Sep 25, 2011 |

Periodic curve as immersed submanifold | Dec 7, 2010 |

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