Metric function and Mathematical function

Metric function noun - A function of a topological space that gives, for any two points in the space, a value equal to the distance between them.

Mathematical function and metric function are semantically related. In some cases you can use "Mathematical function" instead a noun phrase "Metric function".

Mathematical function noun - Mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function.

Metric function and mathematical function are semantically related. Sometimes you can replace phrase "Metric function" with "Mathematical function", this phrases are similar.