Complete accumulation point

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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 $M$.


[ArPo] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) (Translated from Russian) Zbl 0568.54001
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Complete accumulation point. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article