Theorem 7.5. A function f : Rstd Rstd is continuous if and only if for every point x in R and ɛ > 0, there is a 8 > 0 such that for every y E R with d(x, y) < 8, then d(f(x), f(y)) < ɛ.
Theorem 7.5. A function f : Rstd Rstd is continuous if and only if for every point x in R and ɛ > 0, there is a 8 > 0 such that for every y E R with d(x, y) < 8, then d(f(x), f(y)) < ɛ.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.3: Properties Of Composite Mappings (optional)
Problem 6E: 6. a. Give an example of mappings and , different from those in Example , where is one-to-one, is...
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