{
  "id": "metric-space",
  "domain": "topology",
  "type": "Concept",
  "title": "Metric Space",
  "slug": "metric-space",
  "url": "/mathematics/topology/metric-space/",
  "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.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Rudin, W. (1976). Principles of Mathematical Analysis. 3rd ed. McGraw-Hill."
    },
    {
      "tier": 1,
      "citation": "Sutherland, W.A. (2009). Introduction to Metric and Topological Spaces. 2nd ed."
    },
    {
      "tier": 2,
      "citation": "Munkres, J.R. (2000). Topology. 2nd ed."
    },
    {
      "tier": 3,
      "citation": "Bryant, V. (1985). Metric Spaces: Iteration and Application."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}