Metric Space

up:: 026 MOC Topology

A metric space is a double $(X,d)$ where $X$ is a (non-empty) set and $d:X\times X:{\mathbb{R}}_0^{+}$ is a Metric Function.

Examples of metric spaces

A trivial example (and initial motivation) is ${\mathbb{R}}^n$ with the Euclidean metric.

Note that Different metrics yield different metric spaces, even over the same base space $X$.

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References

• Sutherland, Wilson A. Introduction to metric and topological spaces. Oxford University Press, 2009.
• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 24