Let the definition of disconnected be the definition in the picture attached. Show that this definition is true if and only if there are nonempty sets A and B, open in E, such that E=AUB and the intersection of A and B is empty. Definition: A subset E of a metric space (X, d) is called dicconnected if thereexist subsets A and B of X which satisfy the following properties:(i) EAUB.(ii) A ‡ Ø and B ‡ Ø.(iii) AnB = 0 and B₁Ā = Ø.-

Answered: Image /qna-images/answer/4183f0c7-1f32-4310-ac2c-ab21358c75e8.jpg

Let the definition of disconnected be the definition in the picture attached. Show that this definition is true if and only if there are nonempty sets A and B, open in E, such that E=AUB and the intersection of A and B is empty.

Let the definition of disconnected be the definition in the picture attached. Show that this definition is true if and only if there are nonempty sets A and B, open in E, such that E=AUB and the intersection of A and B is empty.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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