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Rational sequence topology

Mathematical theory related to general topology From Wikipedia, the free encyclopedia

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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[1] is specified by letting each rational number singleton to be open, and using as a neighborhood base for each irrational number x, the sets

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