Difference between revisions of "Discrete topology"
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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]]. | ||
| − | [[Category: | + | 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>. |
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| + | [[Category:Topology]] | ||
Latest revision as of 04:22, January 7, 2017
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 .
