[1] Every subsequential limit is a cluster point, but not conversely.
In first-countable spaces, the two concepts coincide.
In a topological space, if every subsequence has a subsequential limit to the same point, then the original sequence also converges to that limit.
Similarly, the infimum of such a set is called the limit inferior, or liminf.
is a metric space and there is a Cauchy sequence such that there is a subsequence converging to some