Examples
The finest topology on X is the discrete topology; this topology makes all subsets open. The coarsest topology on X is the trivial topology; this topology only admits the null set and the whole space as open sets.
In function spaces and spaces of measures there are often a number of possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships.
All possible polar topologies on a dual pair are finer than the weak topology and coarser than the strong topology.
Read more about this topic: Comparison Of Topologies
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