# self-intersections of a curve

## self-intersections of a curve

Let $X$ be a topological manifold and $\gamma:[0,1]\rightarrow X$ 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 $a\neq b$ 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 SelfintersectionsOfACurve 2013-03-22 14:01:11 2013-03-22 14:01:11 mike (2826) mike (2826) 9 mike (2826) Definition msc 57N16 msc 57R42