metric map

Then there exists a natural metric map such that :

The epimorphisms are the metric maps in which the domain of the map has a dense image in the range.

Let be the space of all real valued metric maps (non-contractive) of .

The composite of metric maps is also metric.

The following representations of metric maps are implemented:

The monomorphisms in Met are the injective metric maps, maps that do not map two points into a single point.

The isomorphisms are the isometries, metric maps that are one-to-one, onto, and distance-preserving.

This is a category because the composition of two metric maps is again a metric map.

The metric maps are both uniformly continuous and Lipschitz, with Lipschitz constant at most one.

A metric map is strictly metric if the above inequality is strict for all x and y in X.

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

A metric space is injective if and only if it is an injective object in the category of metric spaces and metric maps.

In the mathematical theory of metric spaces, a metric map is a function between metric spaces that does not increase any distance (such functions are always continuous).

For this reason, the MLRS is sometimes referred to as the "Grid Square Removal System" (metric maps are usually divided up into 1 km grids).

The "forgetful" functor Met Set assigns to each metric space the underlying set of its points, and assigns to each metric map the underlying set-theoretic function.

There has always been some uncertaincy about which is the highest point, with both An Gearanach and An Garbhanach given a height of 3,200 feet on pre metric maps in the 1970s.

In category-theoretic mathematics, 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 distance) as its morphisms.

Isbell was the first to study the category of metric spaces defined by metric spaces and the metric maps between them, and did early work on injective metric spaces and the tight span construction.

Thus metric spaces and metric maps form a category Met; Met is a subcategory of the category of metric spaces and Lipschitz functions, and the isomorphisms in Met are the isometries.