# self-intersections of a curve

## self-intersections of a curve

Let $X$ be a topological manifold^{} and $\gamma :[0,1]\to X$ a segment of a curve in $X$.

Then the curve is said to have a self-intersection in a point $p\in X$ if $\gamma $ fails to be injective, i.e. if there exists $a,b\in (0,1)$, with $a\ne b$ such that $\gamma (a)=\gamma (b)$. Usually, the case when the curve is closed i.e. $\gamma (0)=\gamma (1)$, is not considered as a self-intersecting curve.

Title | self-intersections of a curve |
---|---|

Canonical name | SelfintersectionsOfACurve |

Date of creation | 2013-03-22 14:01:11 |

Last modified on | 2013-03-22 14:01:11 |

Owner | mike (2826) |

Last modified by | mike (2826) |

Numerical id | 9 |

Author | mike (2826) |

Entry type | Definition |

Classification | msc 57N16 |

Classification | msc 57R42 |