In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details. Two metric spaces are …

Isometry, in mathematics, refers to a distance-preserving transformation. Isometry may also refer to: Isometry between quadratic spaces; Isometry group; Quasi-isometry; Dade isometry; …

距離空間 X, Y の間に距離を保つ全単射 (isometry) が存在するとき、 X と Y は距離空間として等長 (isometric) であるという。 また、距離空間 X からそれ自身への距離を保つ全単射を X 上 …

May 14, 2018 · An isometry is a shape preserving transformation. Rotations and reflections are two examples. A dilation is not an isometry because it changes the size of the shape.

Nov 11, 2022 · Isometry: a map that preserves norms. So, if T: X → Y T: X → Y is an isometry among normed linear spaces, then ∥Tx∥Y =∥x∥X ‖ T x ‖ Y = ‖ x ‖ X. In the context of vector …

Jan 8, 2017 · It seems that isometry does not have to be bijective (surjective) as I learnt from my lecture. But why on https://en.wikipedia.org/wiki/Isometry_(Riemannian_geometry) defined …

Apr 4, 2023 · An isometry preserves distances, so since distinct points are at a positive distance from one another, they are mapped to distinct points in the image. (In particular, an isometry …

Sep 2, 2019 · This definition from wikipedia adds to my confusion: If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the …

In matematica, una isometria (dal greco ἴσος, isos, che significa uguale) è una nozione che generalizza quella di movimento rigido di un oggetto o di una figura geometrica. Formalmente, …

Jul 15, 2017 · Wikipedia's definition differs formally, but is equivalent: Either definition implies geodesic completeness. If p p and q q are arbitrary, let γ γ be a minimizing geodesic from p p …

En géométrie, une isométrie est une transformation géométrique qui conserve les longueurs, et les mesures des angles délimités par deux demi‑droites ou bien deux demi‑plans. Autrement …

În matematică o izometrie (sau congruență, sau transformare congruentă) este o transformare în spații metrice care conservă distanța, transformare presupusă de obicei a fi bijectivă. [2]

For an isometry, it is easy to see that for every $x\in X$, we have $$f^{-1}\bigl( B_\varepsilon\left(f(x)\right)\bigr) = B_\varepsilon(x),$$ so $f$ is continuous at $x$, and since …

Eine Isometrie ist in der Mathematik eine Abbildung, die zwei metrische Räume aufeinander abbildet und dabei die Metrik erhält. Das heißt, der Abstand zweier Bildpunkte ist gleich groß …