In a topological space $X$, quoted from Wikipedia:
A point $x ∈ X$ is a cluster point of a sequence $(x_n)_{n ∈ N}$ if, for every neighbourhood $V$ of $x$, there are infinitely many natural numbers $n$ such that $x_n ∈ V$. If the space is sequential, this is equivalent to the assertion that $x$ is a limit of some subsequence of the sequence $(x_n)_{n ∈ N}$.
I was wondering when a topological space is not necessarily sequential, what is the relation between cluster point of a sequence and limit point of some subsequence of the sequence?
When the topological space is sequential space, why are the two equivalent?
Thanks and regards!