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In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.
In mathematics, metric may refer to one of two related, but distinct concepts: A function which measures distance between two points in a metric space A metric tensor , in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold
The basic units of the metric system have always represented commonplace quantities or relationships in nature; even with modern refinements of definition and methodology. In cases where laboratory precision may not be required or available, or where approximations are good enough, the commonplace notions may suffice.
Metric units are units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. According to Schadow and McDonald, [ 1 ] metric units, in general, are those units "defined 'in the spirit' of the metric system, that emerged in late 18th century France and was rapidly adopted by scientists and engineers.
In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. Much of analysis happens in some metric space; the most commonly used are the real line, the complex plane, Euclidean space, other vector spaces, and the integers.
A metric: there is a notion of distance between points. A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field.
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In mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. [1] This is equivalent to: A connection for which the covariant derivatives of the metric on E ...