Isolated points are points in a set that have no other points in their immediate vicinity. They are "isolated" because they are not surrounded by any other points.
Unlike other points, isolated points have no neighboring points within a certain distance. They stand alone and do not form any kind of pattern or cluster.
Isolated points are important in topology and real analysis, as they help define the concept of continuity. A function is continuous at a point if and only if the point is not isolated.
Yes, isolated points can exist in a continuous function. However, the function must have some other points that are not isolated in order to be considered continuous.
In a set of data, isolated points can be identified by plotting the points on a graph and looking for points that are not part of any pattern or trend. They can also be identified by calculating the distance between points and identifying any points with a significantly larger distance to their nearest neighbor.