Definition:Metric Space/Notation

Metric Space: Notation

Some authors use the suboptimal $M = \set {A, d}$, which leaves it conceptually unclear as to which is the set and which the metric.

This adds unnecessary complexity to the underlying axiomatic justification for the existence of the very object that is being defined.

The notation $M = \eqclass {A, \rho} {}$ can also be found.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.1$: Motivation: Definition $2.1.2$