In topological space $X$, the cluster point $s$ of a net $S$ is that $S$ is frequently in every neighborhood of $s$. It is obvious that if $s$ is a cluster point of $S$, then it is the limit point of it, is the converse true?
In Kelly's book, it states that the collection of cluster points of $S$ is exactly the intersection of the collection of limit points of $A_n$, where $A_n=\{S_m|m\geq n\}$. However, I don't think it solve the problem.