**Exercise 4.4:** Prove that a topological space \( X \) is disconnected if and only if there exists a nonconstant continuous function from \( X \) to the discrete space \(\{0, 1\}\).

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Answered: ► Exercise 4.4. Prove that a…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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► Exercise 4.4. Prove that a topological space X is disconnected if and only there exists a nonconstant continuous function from X to the discrete space {0, 1}.