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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.

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.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.2: Real Numbers
Problem 3E: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...
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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.
Transcribed Image Text: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.
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