Definition: A set XCR is said to be disconnected if there exists disjoint open sets U and V such that XCUUV, XNU 0, and XV 0. A set is said to be connected if it is not disconnected. Let f: RR be continuous and XCR be connected. Prove f(X) is connected.
Definition: A set XCR is said to be disconnected if there exists disjoint open sets U and V such that XCUUV, XNU 0, and XV 0. A set is said to be connected if it is not disconnected. Let f: RR be continuous and XCR be connected. Prove f(X) is connected.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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