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self-intersections of a curve
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(Definition)
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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.
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"self-intersections of a curve" is owned by mike. [ full author list (2) | owner history (1) ]
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Cross-references: closed, injective, point, curve, segment, topological manifold
This is version 6 of self-intersections of a curve, born on 2003-10-15, modified 2004-04-05.
Object id is 4959, canonical name is SelfIntersectionsOfACurve.
Accessed 1558 times total.
Classification:
| AMS MSC: | 57N16 (Manifolds and cell complexes :: Topological manifolds :: Geometric structures on manifolds) | | | 57R42 (Manifolds and cell complexes :: Differential topology :: Immersions) |
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Pending Errata and Addenda
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