A set X with distance d: X×X → ℝ≥0 satisfying identity, symmetry, and triangle inequality. Every metric induces a topology; not every topology comes from a metric.
Metric space (X, d)
Related concepts
- Open set
- Real numbers (ℝ)
- Uniform continuity
- Banach fixed-point theorem
- Baire category theorem
- Minimax uniform approximation
- Direct method (Tonelli)
- Blaschke selection theorem
- Banach-Steinhaus uniform boundedness
- Fréchet + locally convex spaces
- Computable real analysis (Weihrauch)
- Standard-siren Hubble: H_0 = c z/d_L (low-z limit); luminosity distance via metric
- Analog quantum simulator: engineered H_device ≈ H_target
- Neighbour-joining
- Levenshtein edit distance: min{ins, del, sub} ops; metric on Σ*
- Mismatch-repair (MMR) framework