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Definitions of accumulation point:
noun: (topology, "of" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S.
noun: (mathematical analysis, "of" a sequence) Given a sequence sᵢ, a point x whose every neighborhood contains at least one element of the sequence distinct from x.
noun: (systems theory, dynamical systems, chaos theory) For certain maps, a point beyond which periodic orbits give way to chaotic ones.