Similarly, a filter on a set contains those subsets that are sufficiently large to contain some given . For example, if is the real line and , then the family of sets including in their interior is a filter, called the neighborhood filter at . The in this case is slightly larger than , but it still does not contain any other specific point of the line.
Similarly, a filter on a set contains those subsets that are sufficiently large to contain some given . For example, if is the real line and , then the family of sets including in their interior is a filter, called the neighborhood filter at . The in this case is slightly larger than , but it still does not contain any other specific point of the line.