# Coarser and Finer Topology

If and are two topologies defined on the non empty set X such that , i.e. each member of is 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.