Category of metric spaces information

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

a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis...

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

in the category of metric spaces bounded by 1 and short maps. That is, any function from a discrete metric space to another bounded metric space is Lipschitz...

distance metric. In contrast, infinite-dimensional normed vector spaces may or may not be complete; those that are complete are Banach spaces. The space C[a...

displaying wikidata descriptions as a fallback Category of metric spaces – mathematical category with metric spaces as its objects and distance-non-increasing...

generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak Hausdorff spaces. Like many categories, the category...

metrizable spaces is a subcategory of that of topological spaces, while the category of complete metric spaces is not (instead, it is a subcategory of the category...

In mathematics, a product metric is a metric on the Cartesian product of finitely many metric spaces ( X 1 , d X 1 ) , … , ( X n , d X n ) {\displaystyle...

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

According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Baire spaces. The Baire category theorem combined...

In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous...

Hilbert spaces Category of sets and relations Category of topological spaces Category of metric spaces Category of preordered sets Category of groups Category...

theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic metric Category of metric spaces Stone duality...

compact Hausdorff space is a Baire space. Neither of these statements directly implies the other, since there are complete metric spaces that are not locally...

complete metric spaces, a set is compact if and only if it is closed and totally bounded. Each totally bounded space is bounded (as the union of finitely...

of timekeeping during space missions Modular Equipment Transporter (Apollo program), lunar handcart Met, the category of metric spaces having metric maps...

completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate...

of the Minkowski metric η under inclusion, is a Riemannian metric. With this metric H1(n) R is a Riemannian manifold. It is one of the model spaces of...

Cauchy space is a generalization of metric spaces and uniform spaces for which the notion of Cauchy convergence still makes sense. Cauchy spaces were introduced...

and finitely cocomplete. The category of complete lattices is complete but not cocomplete. The category of metric spaces, Met, is finitely complete but...

metric spaces need not be the same). And since any Euclidean space is complete, we can thus conclude that all finite-dimensional normed vector spaces...

toward the construction of the metric envelope, or tight span, which are basic (injective) objects of the category of metric spaces. Following (Holsztyński...

of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental,...

compactification. The category of all complete metric spaces with uniformly continuous mappings is a reflective subcategory of the category of metric spaces. The reflector...

In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d ( x , z ) ≤ max { d ( x , y ) , d ( y , z...

metric (FLRW), where it corresponds to an increase in the scale of the spatial part of the universe's spacetime metric tensor (which governs...

irrespective of the spaces being tensored: this implies that any space with a tensor product is a symmetric monoidal category, and Hilbert spaces are a particular...