The uniform one of these induces a topology on Euclidean space that is finer than the product topology and coarser than the box topology.
The uniform one of these induces a topology on Euclidean space that is finer than the product topology and coarser than the box topology. One of these can be defined for any regular space with a countable basis, according to the Urysohn theorem. The discrete topology corresponds to one of these functions that gives 0 for identical points and 1 for any distinct pair of points. One of these can be defined in terms of a norm as the norm of the difference of the arguments. FTP name these positive-definite, symmetric functions that obey the triangle inequality and give the distance between any pair of points in a space.
The uniform one of these induces a topology on Euclidean space that is finer than the product topology and coarser than the box topology.
{metric}s