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