complete metric space - определение. Что такое complete metric space
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Что (кто) такое complete metric space - определение

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Complete metric space         
METRIC SPACE IN WHICH CAUCHY SEQUENCE CONVERGES TO AN ELEMENT OF THE SPACE
Complete metric; Completeness (topology); Completion (topology); Complete (topology); Cauchy complete; Cauchy complete space; Cauchy completion; Cauchy completeness; Completion (metric space); Banach completion; Completeness (in topology); Complete space; Metric space completion; Completion of a metric space; Complete pseudometric space; Complete pseudometric
In mathematical analysis, a metric space is called complete (or a Cauchy space) if every Cauchy sequence of points in has a limit that is also in .
complete metric space         
METRIC SPACE IN WHICH CAUCHY SEQUENCE CONVERGES TO AN ELEMENT OF THE SPACE
Complete metric; Completeness (topology); Completion (topology); Complete (topology); Cauchy complete; Cauchy complete space; Cauchy completion; Cauchy completeness; Completion (metric space); Banach completion; Completeness (in topology); Complete space; Metric space completion; Completion of a metric space; Complete pseudometric space; Complete pseudometric
<theory> A metric space in which every sequence that converges in itself has a limit. For example, the space of real numbers is complete by Dedekind's axiom, whereas the space of rational numbers is not - e.g. the sequence a[0]=1; a[n_+1]:=a[n]/2+1/a[n]. (1998-07-05)
Metric space         
  • Diameter of a set.
  • [[Euler diagram]] of types of functions between metric spaces.
  • Q}} on a sphere.
SET EQUIPPED WITH A METRIC (DISTANCE FUNCTION)
Distance function; Metric spaces; Metric topology; Metric geometry; Bounded metric space; Bounded metric; Bounded space; Metric (mathematics); Quasimetric space; Translation-invariant metric; Translation invariant metric; Semi-metric; Semi metric space; Homogeneous metric; Quotient metric space; Semimetric; Postoffice metric; Post office metric; British rail metric; SNCF metric; Quasimetric; Quasi-metric; Premetric space; Prametric; Hemimetric space; Hemimetric; Semimetric space; Hemi-metric; Prametrizable; Distance to a set; Metric distance; General metric; Relation of norms and metrics; Inframetric; Post Office metric; Prametric space; Premetric; Finite metric space; Discrete metric space; Metric Geometry; Distance metric; Pseudoquasimetric space; Pseudo-semimetric; French railway metric; British Rail metric; Norm induced metric; Diameter of a metric space; Generalizations of metric spaces; Metric embeddings
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.
Metric (mathematics)         
  • Diameter of a set.
  • [[Euler diagram]] of types of functions between metric spaces.
  • Q}} on a sphere.
SET EQUIPPED WITH A METRIC (DISTANCE FUNCTION)
Distance function; Metric spaces; Metric topology; Metric geometry; Bounded metric space; Bounded metric; Bounded space; Metric (mathematics); Quasimetric space; Translation-invariant metric; Translation invariant metric; Semi-metric; Semi metric space; Homogeneous metric; Quotient metric space; Semimetric; Postoffice metric; Post office metric; British rail metric; SNCF metric; Quasimetric; Quasi-metric; Premetric space; Prametric; Hemimetric space; Hemimetric; Semimetric space; Hemi-metric; Prametrizable; Distance to a set; Metric distance; General metric; Relation of norms and metrics; Inframetric; Post Office metric; Prametric space; Premetric; Finite metric space; Discrete metric space; Metric Geometry; Distance metric; Pseudoquasimetric space; Pseudo-semimetric; French railway metric; British Rail metric; Norm induced metric; Diameter of a metric space; Generalizations of metric spaces; Metric embeddings
In mathematics, a metric or distance function is a function that gives a distance between each pair of point elements of a set. A set with a metric is called a metric space.
Metrics (networking)         
FIELD IN A ROUTING TABLE, USED BY A ROUTER TO MAKE ROUTING DECISIONS
Routing Metric; Router metrics; Routing metric
Router metrics are configuration values used by a router to make routing decisions. A metric is typically one of many fields in a routing table.
metric system         
  • [[Pavillon de Breteuil]], Saint-Cloud, France, the home of the metric system since 1875
  • [[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.
  • The [[metre]] was originally defined to be ''one ten millionth'' of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]].<ref name=Alder />
DECIMAL SYSTEM OF UNITS THAT USES THE METRE AS THE BASIS FOR ITS UNIT OF LENGTH
Metric unit; Metric System; Metric measurement system; The Metric System; Metric conversions; Metric system of measurement; Metric weights and measures; Metrics system; SI symbol; Symbol (metric system); Symbol (metric); Symbols (metric); Symbols (metric system); Metric symbol; Metric symbols; Metric measurements; Mètrique; French metrical system; Metric system of weights and measures
¦ noun the decimal measuring system based on the metre, litre, and gram as units of length, capacity, and weight or mass.
metric system         
  • [[Pavillon de Breteuil]], Saint-Cloud, France, the home of the metric system since 1875
  • [[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.
  • The [[metre]] was originally defined to be ''one ten millionth'' of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]].<ref name=Alder />
DECIMAL SYSTEM OF UNITS THAT USES THE METRE AS THE BASIS FOR ITS UNIT OF LENGTH
Metric unit; Metric System; Metric measurement system; The Metric System; Metric conversions; Metric system of measurement; Metric weights and measures; Metrics system; SI symbol; Symbol (metric system); Symbol (metric); Symbols (metric); Symbols (metric system); Metric symbol; Metric symbols; Metric measurements; Mètrique; French metrical system; Metric system of weights and measures
The metric system is the system of measurement that uses metres, grams, and litres.
N-SING: the N
Metric system         
  • [[Pavillon de Breteuil]], Saint-Cloud, France, the home of the metric system since 1875
  • [[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.
  • The [[metre]] was originally defined to be ''one ten millionth'' of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]].<ref name=Alder />
DECIMAL SYSTEM OF UNITS THAT USES THE METRE AS THE BASIS FOR ITS UNIT OF LENGTH
Metric unit; Metric System; Metric measurement system; The Metric System; Metric conversions; Metric system of measurement; Metric weights and measures; Metrics system; SI symbol; Symbol (metric system); Symbol (metric); Symbols (metric); Symbols (metric system); Metric symbol; Metric symbols; Metric measurements; Mètrique; French metrical system; Metric system of weights and measures
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body.
Metric system         
  • [[Pavillon de Breteuil]], Saint-Cloud, France, the home of the metric system since 1875
  • [[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.
  • The [[metre]] was originally defined to be ''one ten millionth'' of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]].<ref name=Alder />
DECIMAL SYSTEM OF UNITS THAT USES THE METRE AS THE BASIS FOR ITS UNIT OF LENGTH
Metric unit; Metric System; Metric measurement system; The Metric System; Metric conversions; Metric system of measurement; Metric weights and measures; Metrics system; SI symbol; Symbol (metric system); Symbol (metric); Symbols (metric); Symbols (metric system); Metric symbol; Metric symbols; Metric measurements; Mètrique; French metrical system; Metric system of weights and measures
·- ·see Metric, ·adj.
metric space         
  • Diameter of a set.
  • [[Euler diagram]] of types of functions between metric spaces.
  • Q}} on a sphere.
SET EQUIPPED WITH A METRIC (DISTANCE FUNCTION)
Distance function; Metric spaces; Metric topology; Metric geometry; Bounded metric space; Bounded metric; Bounded space; Metric (mathematics); Quasimetric space; Translation-invariant metric; Translation invariant metric; Semi-metric; Semi metric space; Homogeneous metric; Quotient metric space; Semimetric; Postoffice metric; Post office metric; British rail metric; SNCF metric; Quasimetric; Quasi-metric; Premetric space; Prametric; Hemimetric space; Hemimetric; Semimetric space; Hemi-metric; Prametrizable; Distance to a set; Metric distance; General metric; Relation of norms and metrics; Inframetric; Post Office metric; Prametric space; Premetric; Finite metric space; Discrete metric space; Metric Geometry; Distance metric; Pseudoquasimetric space; Pseudo-semimetric; French railway metric; British Rail metric; Norm induced metric; Diameter of a metric space; Generalizations of metric spaces; Metric embeddings
<mathematics> A set of points together with a function, d, called a metric function or distance function. The function assigns a positive real number to each pair of points, called the distance between them, such that: 1. For any point x, d(x,x)=0; 2. For any two distinct points x and y, d(x,y) > 0; 3. For any two points x and y, not necessarily distinct, d(x,y) = d(y,x). 4. For any three points x, y, and z, that are not necessarily distinct, d(x,z) <= d(x,y) + d(y,z). The distance from x to z does not exceed the sum of the distances from x to y and from y to z. The sum of the lengths of two sides of a triangle is equal to or exceeds the length of the third side. (2003-06-26)