ed. Proof omitted.) iformly continuous to
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 6TFE: Label each of the following statements as either true or false. Let g:AB and f:BC such that fg is...
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Question
![Assume the following statement:
If a function f: (a,b) → R is uniformly continuous, then both f(a+) and f(b-)
are finite.
(This is true. Take as granted. Proof omitted.)
Can we change the term uniformly continuous to continuous in the assumption?
Justify prove if yes, give a counterexample if no.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0a8204-4fa5-4052-9ac3-10c50e7b25a4%2F804bdb5d-5fe6-4ed6-ac89-163fa516b9a2%2Fng9j2pk_processed.png&w=3840&q=75)
Transcribed Image Text:Assume the following statement:
If a function f: (a,b) → R is uniformly continuous, then both f(a+) and f(b-)
are finite.
(This is true. Take as granted. Proof omitted.)
Can we change the term uniformly continuous to continuous in the assumption?
Justify prove if yes, give a counterexample if no.
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