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Difference between revisions of "Complete accumulation point"

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''of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237001.png" /> in a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237002.png" />''
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A point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237003.png" /> such that the intersection of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237004.png" /> with any neighbourhood of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237005.png" /> has the same cardinality as the entire set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023700/c0237006.png" />.
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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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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"A.V. Arkhangel'skii,   V.I. Ponomarev,   "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></TR></table>
 

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