Exercise 4. A subset A of a topological space X is called dense if cl A = X. Theset Q of rational numbers and the set R \ Q of irrational numbers are both subset ofthe real line. Show that they are both dense in the real line with its usual topology.

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Answered: Exercise 4. A subset A of a topological…

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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Exercise 4. A subset A of a topological space X is called dense if cl A = X. The set Q of rational numbers and the set R\Q of irrational numbers are both subset of the real line. Show that they are both dense in the real line with its usual topology.