Suuntansäilyttävässä
Suuntansäilyttävä, a Finnish term, translates to "direction-preserving" or "orientation-preserving" in English. This concept is fundamental in various fields of mathematics, particularly in geometry and topology. A function or transformation is considered suuntansäilyttävä if it preserves the orientation of spaces. This means that if a region is oriented clockwise in the original space, its image under the suuntansäilyttävä transformation will also be oriented clockwise in the transformed space, and similarly for counter-clockwise orientations.
In Euclidean geometry, transformations like rotations and translations are suuntansäilyttävä. These transformations do not flip the
The concept is crucial in differential geometry when studying manifolds. A diffeomorphism (a differentiable map with