# Difference between revisions of "Complete accumulation point"

From Encyclopedia of Mathematics

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− | A point | + | A complete accumulation point of a set $M$ in a topological space $X$ is a point $x\in X$ such that the intersection of $M$ with any neighbourhood of $x$ has the same cardinality as the entire set $M$. |

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− | + | |valign="top"|{{Ref|ArPo}}||valign="top"| A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) (Translated from Russian) | |

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## Revision as of 23:16, 24 July 2012

2010 Mathematics Subject Classification: *Primary:* 54Axx [MSN][ZBL]

A complete accumulation point of a set $M$ in a topological space $X$ is a point $x\in X$ such that the intersection of $M$ with any neighbourhood of $x$ has the same cardinality as the entire set $M$.

#### References

[ArPo] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) (Translated from Russian) |

**How to Cite This Entry:**

Complete accumulation point.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Complete_accumulation_point&oldid=27203

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article