Category of metric spaces with continuous maps

Definition
The category of metric spaces with continuous maps is defined as follows:


 * The objects of this category are metric spaces.
 * The morphisms of this category are continuous maps of metric spaces.

Related categories

 * Category of topological spaces with continuous maps: In fact, we have a forgetful functor from the category of metric spaces with continuous maps to the category of topological spaces with continuous maps.
 * Category of metric spaces with uniformly continuous maps: This is a subcategory with the same objects and fewer morphisms.
 * Category of metric spaces with short maps: This is a subcategory with the same objects and fewer morphisms.