Definition: A set X C R is said to be disconnected if there exists disjoint open sets U and V such that X CUUV, X NU Ø, and X n V + Ø. A set is said to be connected if it is not disconnected. Let ƒ : R → R and X C R be connected. Prove f(X) is connected.

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Definition: A set X CR is said to be disconnected if there exists disjoint open
sets U and V such that X CUUV, X N U + Ø, and X NV + Ø. A set is said to be
connected if it is not disconnected.
Let f : R → R and X C R be connected. Prove f(X) is connected.
Transcribed Image Text:Definition: A set X CR is said to be disconnected if there exists disjoint open sets U and V such that X CUUV, X N U + Ø, and X NV + Ø. A set is said to be connected if it is not disconnected. Let f : R → R and X C R be connected. Prove f(X) is connected.
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