If , then is called a limit (point) of . The prefilter is said to cluster at (or have as a cluster point) if and only if each element of has non-empty intersection with each neighborhood of . Every limit point is a cluster point but the converse is not true in general. However, every cluster point of an filter is a limit point.
If , then is called a limit (point) of . The prefilter is said to cluster at (or have as a cluster point) if and only if each element of has non-empty intersection with each neighborhood of . Every limit point is a cluster point but the converse is not true in general. However, every cluster point of an filter is a limit point.