Exercise 1. Give examples of subsets A, B in a topological space X (for example X = R or X = R²) such that:} ed. (c) Both A and B are not connected, but AUB is connected. connected.
Exercise 1. Give examples of subsets A, B in a topological space X (for example X = R or X = R²) such that:} ed. (c) Both A and B are not connected, but AUB is connected. connected.
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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1C
![**Exercise 1:** *Give examples of subsets \(A, B\) in a topological space \(X\) (for example \(X = \mathbb{R}\) or \(X = \mathbb{R}^2\)) such that:*
(a) [Text covered]
(b) [Text covered]
(c) Both \(A\) and \(B\) are not connected, but \(A \cup B\) is connected.
(d) [Text covered]
*Note: Some parts of the text have been intentionally obscured and are not accessible for transcription.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F44e0bbd9-1014-40c5-aa11-a9fb1eb4c51e%2F3b4ezq9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 1:** *Give examples of subsets \(A, B\) in a topological space \(X\) (for example \(X = \mathbb{R}\) or \(X = \mathbb{R}^2\)) such that:*
(a) [Text covered]
(b) [Text covered]
(c) Both \(A\) and \(B\) are not connected, but \(A \cup B\) is connected.
(d) [Text covered]
*Note: Some parts of the text have been intentionally obscured and are not accessible for transcription.*
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