Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let (X, d) be a metric space. A subset E of X is called pathwise connected if for every €₁, €2 € E, there exists a continuous function e : [0, 1] → E such that e (0) = e₁ and e(1) = €2. Prove that if E C X is pathwise connected then E is connected.
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Transcribed Image Text:Let (X, d) be a metric space. A subset E of X is called pathwise connected if for every €₁, €2 € E, there exists a continuous function e : [0, 1] → E such that e (0) = e₁ and e(1) = €2. Prove that if E C X is pathwise connected then E is connected.
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