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discrete topology is a metric space
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]].
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 <math>d(x, y) = 1</math> if <math>x \neq y</math> and <math>d(x, x) = 0</math>.
[[Category:Topology]]
[[Category:Topology]]