If and  are two topologies defined on the non empty set X such that, i.e. each member ofis also in, then is said to be coarser or weaker than  and is said to be finer or stronger than.

            It may be noted that indiscrete topology defined on the non empty set X is the weakest or coarser topology on that set X and discrete topology defined on the non empty set X is the stronger or finer topology on that set X.

Note: The topology which is both discrete and indiscrete such topology which has one element in set X.

i.e. X = {a}, {, X}. Every singleton set is discrete as well as indiscrete topology on that set.