فضای ِ متریک fazâ-ye metrik
*Fr.: espace métrique*
An set of points such that the distance between every pair of points is defined
by a → *distance function* with
the following properties: 1) the distance from
the first point to the second equals zero if and only if the points
are the same, 2) the distance from the first point to the second
equals the distance from the second to the first, and 3) the sum of
the distance from the first point to the second and the distance from
the second point to a third exceeds or equals the distance from the
first to the third.
In mathematical language, the properties, for a nonempty set *X*, can be
expressed as:
1) *d(x,y)*≥ 0 and *d(x,y)* = 0 if and only if *x = y*.
2) *d(x, y) = d(y,x)* for all *x, y ∈ X*.
3) *d(x,z)*≤ *d(x,y) + d(y,z)* for all *x, y*,
and *z ∈ X*. Also called → *triangle inequality*. → *metric*; → *space*. |