# Metric space/Related Articles

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*See also changes related to Metric space, or pages that link to Metric space or to this page or whose text contains "Metric space".*

## Parent topics

- Space (mathematics) [r]: A set with some added structure, which often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.
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## Subtopics

## Bot-suggested topics

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- Bounded set [r]: A set for which there is a constant
*C*such that the norm of all elements in the set is less than*C*.^{[e]} - Category theory [r]: Loosely speaking, a class of objects and a collection of morphisms which act upon them; the morphisms can be composed, the composition is associative and there are identity objects and rules of identity.
^{[e]} - Cauchy sequence [r]: Sequence in which the distance between two elements becomes smaller and smaller.
^{[e]} - Compact space [r]: A toplogical space for which every covering with open sets has a finite subcovering.
^{[e]} - Compactness axioms [r]: Properties of a toplogical space related to compactness.
^{[e]} - Complete metric space [r]: Property of spaces in which every Cauchy sequence converges to an element of the space.
^{[e]} - Continuity [r]: Property of a function for which small changes in the argument of the function lead to small changes in the value of the function.
^{[e]} - Discrete metric [r]: The metric on a space which assigns distance one to any distinct points, inducing the discrete topology.
^{[e]} - Geometry [r]: The mathematics of spacial concepts.
^{[e]} - Heine–Borel theorem [r]: In Euclidean space of finite dimension with the usual topology, a subset is compact if and only if it is closed and bounded.
^{[e]} - Inner product [r]: A bilinear or sesquilinear form on a vector space generalising the dot product in Euclidean spaces.
^{[e]} - Limit point [r]: A point which cannot be separated from a given subset of a topological space; all neighbourhoods of the points intersect the set.
^{[e]} - Metric [r]:
*Add brief definition or description* - Neighbourhood (topology) [r]: In a topological space, a set containing a given point in its interior, expressing the idea of points "near" this point.
^{[e]} - Norm (mathematics) [r]: A function on a vector space that generalises the notion of the distance from a point of a Euclidean space to the origin.
^{[e]} - P-adic metric [r]: A metric on the rationals in which numbers are close to zero if they are divisible by a large power of a given prime
*p*.^{[e]} - Rational number [r]: A number that can be expressed as a ratio of two integers.
^{[e]} - Real number [r]: A limit of the Cauchy sequence of rational numbers.
^{[e]} - Space (mathematics) [r]: A set with some added structure, which often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.
^{[e]} - Topological space [r]: A mathematical structure (generalizing some aspects of Euclidean space) defined by a family of open sets.
^{[e]} - Totally bounded set [r]: A subset of a metric space with the property that for any positive radius it is coveted by a finite union of open balls of given radius.
^{[e]} - Triangle inequality [r]: Inequality which states that for any triangle, the length of a given side must be less than or equal to the sum of the other two sides but greater than or equal to the difference between the two sides.
^{[e]} - Uniform space [r]: Topological space with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence.
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