Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Definition: A set X ⊆ R is said to be disconnected if there exists disjoint open sets U and V such that X ⊆ U ∪ V, X ∩ U not equal ∅, X ∩ V not equal ∅. A set is said to be connected if it is not disconnected.

 

Let f: R -> R be continuous and X ⊆ R be connected. Prove f(X) is connected.

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