Let be a topological space and be a subset. A point is an adherent point for if every open set containing contains at least one point of . A point is an adherent point for if and only if is in the closure of .
This definition is more general than that of a limit point, in that for a limit point it is required that every open set containing contains at least one point of different from . Thus every limit point is an adherent point, but the converse fails. An adherent point which is not a limit point is an isolated point.
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Membership still has its privileges: voting for elders, ministers off-limits for adherents.(130th General Assembly 2004)
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