Pseudometric Space

up:: 026 MOC Topology

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

Corollaries

All pseudometric spaces induce metric spaces via “quotienting” points with distance $0$ to the same equivalent class.

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 24