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What is a gathering point?
In calculus (mathematical analysis): for any given δ >; 0, there is always a point in E in the centripetal neighborhood U(P, δ) of point P, and the aggregation point called P is E, which is either an inner point or a boundary point.

In a complex variable function: the set of points E. If there are infinite points of E in any neighborhood of a point Z on the complex plane, then Z is called the aggregation point of E..

In topology, let A be a subset of topological space X, X ∈ X. If every neighborhood of X contains points in A\{x}, then X is called the aggregation point of A.

Equivalent definition:

There are infinitely many points in the arbitrary neighborhood of point ξ in the set S, which is called the aggregation point of S.

From Baidu Encyclopedia