mathematical theory of metric spaces, a metric map is a function between metric spaces that does not increase any distance. These maps are the morphisms in...

In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function...

theory, Met is a category that has metric spaces as its objects and metric maps (continuous functions between metric spaces that do not increase any pairwise...

Riemannian metric determines a canonical affine connection, and the exponential map of the (pseudo) Riemannian manifold is given by the exponential map of this...

metric system METRIC, a model that uses Landsat satellite data to compute and map evapotranspiration (ET) in climatology/meteorology The word metric is...

user. The following representations of metric maps are implemented: Occupancy grid maps Point maps Landmark maps: discrete elements are 3D points sensed...

planet earth" Yandex Maps, popular in Russia and CIS Lite version for Android "Google Maps Metrics and Infographics". Google Maps for iPhone. Archived...

precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent...

transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to...

refinement. Metric See Metric space. Metric invariant A metric invariant is a property which is preserved under isometric isomorphism. Metric map If X and...

the metric system of measurement. All over the world, countries have transitioned from local and traditional units of measurement to the metric system...

Euclidean geometry Exponential map Exponential map (Lie theory), Exponential map (Riemannian geometry) Finsler metric A generalization of Riemannian manifolds...

In mathematics, a metric projection is a function that maps each element of a metric space to the set of points nearest to that element in some fixed sub-space...

called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian...

multiplication map G → G sending a point y to xy. Riemannian metrics constructed this way are left-invariant; right-invariant Riemannian metrics could be constructed...

within the same frame of reference or coordinates. Map building can be in the shape of a metric map or any notation describing locations in the robot frame...

1.4.1  of f. If K = 1 the function is called a short map, and if 0 ≤ K < 1 and f maps a metric space to itself, the function is called a contraction...

In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other...

group homomorphisms Category of metric spaces – Category whose objects are metric spaces and whose morphisms are metric maps Category of sets – Category whose...

tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive...

the transform/map is qualified with the chosen metric. For example, one may speak of Manhattan distance transform, if the underlying metric is Manhattan...

In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those...

that diffeomorphic metric maps satisfy the property that the length associated to their flow away from the identity induces a metric on the group of diffeomorphisms...

units or the metric system, to replace a jurisdiction's traditional measuring units. U.S. customary units have been defined in terms of metric units since...

discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded...

this map needs modification (Lee deals with Riemannian metrics.). Where Lee refers to positive definiteness to show the injectivity of the map, one needs...

embedding distorts distances. Suppose that one metric space S is embedded into another metric space T by a metric map, a continuous one-to-one function f that...

generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by Ballmann (1990) for metric spaces of non-positive curvature...

places of the map. Each projection preserves, compromises, or approximates basic metric properties in different ways. The purpose of the map determines which...

diffeomorphism between two Riemannian manifolds is called a conformal map if the pulled back metric is conformally equivalent to the original one. For example,...