 ##  [Accumulation Point](/index.php/accumulation-point) 

  ##  [Accumulation Point](https://natural.quantumdictionary.io/accumulation-point-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/index.php/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A point x in a topological space is an accumulation (limit) point of a set S if every neighbourhood of x contains at least one point of S distinct from x itself; equivalently x belongs to the derived set S' of limit points.

 
 ##  [Accumulation Point](https://mathlogic.quantumdictionary.io/accumulation-point-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A point such that every neighborhood of it contains at least one point of a given set distinct from the point itself (or infinitely many points, depending on convention); equivalently a point in the closure of the set minus any isolated occurrences.

 
 ##  [Accumulation Point](https://puremath.quantumdictionary.io/accumulation-point-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A point such that every neighborhood contains infinitely many distinct points of a given set; equivalently a limit point of the set that is not isolated, often used to describe limiting behavior of sequences and subsets.