In mathematics, a metric or distance function is a function (mathematics)|function which defines a distance between elements of a Set (mathematics)|set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.
In differential geometry, the word metric may refer to a bilinear form that may be defined from the tangent vectors of a differentiable manifold onto a scalar, allowing distances along curves to be determined through integration. It is more properly termed a metric tensor.