But then in this space coordinate corresponding to the time in real space depends on the spatial coordinates of reference points. Try asking an abstract space. Consider the four-dimensional pseudo-Euclidean space F, naprmer, with signature -+++. Center coordinates denote the point O. Coordinates x, y, z - given by the usual three-dimensional Euclidean space. Fourth coordinate any L point of F, denoted by - q, then the point is written as L (q, x, y, z). Consider a space where the coordinate q - function of the coordinates x, y, z: q = R (OL) / c, where c - constant (for example, the speed of light), R (OL) - the length of OL in three-dimensional space with coordinates x, y, z.

From topology we know that: A metric on a set of Y - is defined on the Cartesian product YxY function of d, whose values are real numbers satisfying for any a, b, c of Y the following conditions: 1) d (a, b) = d (b, a). 2) d (a, b) + d (b, c) d (a, c) (triangle inequality). 3) d (a, b) = 0 if a = b. 4) if d (a, b) = 0 then a = b. Function, which satisfies only 1) 2) 3) - is called a pseudometric. Obviously, for our space executed only 1) 2) 3), so F - pseudometric space. Some properties are obvious: a) the sign of the change q coincides with changes in R (OL). b) in this method the coordinates of any distance between two points in the pseudometric space F is zero.

From topology we know that: A metric on a set of Y - is defined on the Cartesian product YxY function of d, whose values are real numbers satisfying for any a, b, c of Y the following conditions: 1) d (a, b) = d (b, a). 2) d (a, b) + d (b, c) d (a, c) (triangle inequality). 3) d (a, b) = 0 if a = b. 4) if d (a, b) = 0 then a = b. Function, which satisfies only 1) 2) 3) - is called a pseudometric. Obviously, for our space executed only 1) 2) 3), so F - pseudometric space. Some properties are obvious: a) the sign of the change q coincides with changes in R (OL). b) in this method the coordinates of any distance between two points in the pseudometric space F is zero.

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