Examples of 2 topologies on a finite set which is weaker than another
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Examples
The prototype
Let X be any metric space and take to be the set of open sets as defined earlier. The properties verified earlier show that  is a topology.
Some "extremal" examples
Take any set X and let  = {, X}. Then is a topology called the trivial topology or indiscrete topology.
Let X be any set and let  be the set of all subsets of X. The  is a topology called the discrete topology. It is the topology associated with the discrete metric.
hope it helps
thanks
have a great day
here is ur answer
Examples
The prototype
Let X be any metric space and take to be the set of open sets as defined earlier. The properties verified earlier show that  is a topology.
Some "extremal" examples
Take any set X and let  = {, X}. Then is a topology called the trivial topology or indiscrete topology.
Let X be any set and let  be the set of all subsets of X. The  is a topology called the discrete topology. It is the topology associated with the discrete metric.
hope it helps
thanks
have a great day
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