Definition
Let (either the open or closed sets does not matter) τ1 and τ2 be two topologies on a set X such that τ1 is contained in τ2:
- .
That is, every element of τ1 is also an element of τ2. Then the topology τ1 is said to be a coarser (weaker or smaller) topology than τ2, and τ2 is said to be a finer (stronger or larger) topology than τ1. If additionally
we say τ1 is strictly coarser than τ2 and τ2 is strictly finer than τ1.
The binary relation ⊆ defines a partial ordering relation on the set of all possible topologies on X.
Read more about this topic: Comparison Of Topologies
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