# Metric Space

**Type:** Concept  
**Domain:** topology  
**Codex URL:** /mathematics/topology/metric-space/  
**Entry status:** Live — v1.0 (2026-07-09)

## Summary
A set with a distance function satisfying 4 axioms (non-negativity, identity, symmetry, triangle inequality). Framework for convergence, continuity, completeness, and compactness. Generalised by topological spaces.

## Sources
- [Tier 1] Rudin, W. (1976). Principles of Mathematical Analysis. 3rd ed. McGraw-Hill.
- [Tier 1] Sutherland, W.A. (2009). Introduction to Metric and Topological Spaces. 2nd ed.
- [Tier 2] Munkres, J.R. (2000). Topology. 2nd ed.
- [Tier 3] Bryant, V. (1985). Metric Spaces: Iteration and Application.

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*Mathematics Codex entry v1.0 — added 2026-07-09 — thecodex.expert/mathematics/*