# Complete metric space/Related Articles

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

## Parent topics

- Topology [r]: A branch of mathematics that studies the properties of objects that are preserved through continuous deformations (such as stretching, bending and compression).
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- Cauchy sequence [r]: Sequence in which the distance between two elements becomes smaller and smaller.
^{[e]} - Metric space [r]: Any topological space which has a metric defined on it.
^{[e]} - Limit of a sequence [r]: A sequence which converges to (or approaches) the limit a as n tends to infinity.
^{[e]} - Banach space [r]: A vector space endowed with a norm that is complete.
^{[e]} - Hilbert space [r]: A complete inner product space.
^{[e]} - Completion [r]:
*Please do not use this term in your topic list, because there is no single article for it. Please substitute a more precise term. See Completion (disambiguation) for a list of available, more precise, topics. Please add a new usage if needed.* - 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.
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- Cauchy (disambiguation) [r]:
*Add brief definition or description* - Discrete metric [r]: The metric on a space which assigns distance one to any distinct points, inducing the discrete topology.
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