Category:Examples of Metric Spaces
Jump to navigation
Jump to search
This category contains examples of Metric Space.
A metric space $M = \struct {A, d}$ is an ordered pair consisting of:
together with:
- $(2): \quad$ a real-valued function $d: A \times A \to \R$ which acts on $A$, satisfying the metric space axioms:
| \((\text M 1)\) | $:$ | \(\ds \forall x \in A:\) | \(\ds \map d {x, x} = 0 \) | ||||||
| \((\text M 2)\) | $:$ | Triangle Inequality: | \(\ds \forall x, y, z \in A:\) | \(\ds \map d {x, y} + \map d {y, z} \ge \map d {x, z} \) | |||||
| \((\text M 3)\) | $:$ | \(\ds \forall x, y \in A:\) | \(\ds \map d {x, y} = \map d {y, x} \) | ||||||
| \((\text M 4)\) | $:$ | \(\ds \forall x, y \in A:\) | \(\ds x \ne y \implies \map d {x, y} > 0 \) |
Subcategories
This category has the following 26 subcategories, out of 26 total.
C
- Chebyshev Distance (27 P)
D
E
- Euclidean Plus Metric (3 P)
F
- Fréchet Product Metric (4 P)
G
H
I
- Irrational Number Space (22 P)
L
P
- P-adic Metrics (5 P)
R
S
- Scaled Euclidean Metric (3 P)
- Standard Discrete Metric (12 P)
T
W
- Word Metric (1 P)
Pages in category "Examples of Metric Spaces"
The following 8 pages are in this category, out of 8 total.