Rational sequence topology
{{short description|Mathematical theory related to general topology}}
In mathematics, more specifically general topology, the rational sequence topology is an example of a topology given to the set R of real numbers.
Construction
For each irrational number x take a sequence of rational numbers {xk} with the property that {xk} converges to x with respect to the Euclidean topology.
The rational sequence topology{{Citation|first=L. A.|last=Steen|first2=J. A.|last2=Seebach|title=Counterexamples in Topology|publisher=Dover|year=1995|page=87|ISBN=0-486-68735-X}} is specified by letting each rational number singleton to be open, and using as a neighborhood base for each irrational number x, the sets
References
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