The discrete topology on a set X makes every point x in X an open subset of X. This is the topology on X with the greatest cardinality.
A topological space with the discrete topology is a metric space, with the metric 
if 
and 
.
The discrete topology on a set X makes every point x in X an open subset of X. This is the topology on X with the greatest cardinality.
A topological space with the discrete topology is a metric space, with the metric if and .