1-variety - 1-variedad
In topology a 1- manifold is a topological space of dimension one.
For example, the number line ^{[ 1 ]} and the circumference ^{[ 2 ]} are 1-manifolds without boundary while the intervals ( bounded ) are 1-manifolds with boundary.
It is also true that the trajectories (not necessarily differentiable) and that they do not intersect themselves, are topological 1-dimensional varieties .
Classification
From the topological point of view we have - for one- connected manifolds - the following homeomorphic types :
- to the number line : infinitely long sets (bi-laterally) and without boundary .
- to the ray : infinitely long sets (uni-laterally) and with a border of a single point.
- at intervals : infinite but bounded sets, with two boundaries of two disjoint points.
- to the circle : infinite, bounded and borderless sets.
For the disconnected they take any of the types above to find the appropriate combination.
Related notions
- curve
- trajectory
- Circle or 1-sphere
- naked
- Toric Nudo
- link
- trenza (braid)
- fundamental group
- group of braids
Notes and references
- ↑ ie the real numbers .
- ↑ In English: circle, cercle, Kreis .