Cauchy sequence
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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![Let Y = R([a, b]) be the set (actually a vector space) of bounded,
real-valued, Riemann integrable functions on the closed and bounded
interval [a, b], and let X = C([a, b]), be the subset (actually a vector
subspace) of continuous, real-valued functions on [a, b]. For f, g = Y,
define
d(f,g) = sup |f(x) — g(x)|.
x= [a,b]
Does every uniformly Cauchy sequence in R([a, b]) converge uni-
formly to a function in R([a, b])?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e8ed93-7bef-4409-89ed-52264f64a27e%2F9bea4f06-3e82-4413-922a-6bb515eb8eeb%2F8z9a1vb_processed.png&w=3840&q=75)
Transcribed Image Text:Let Y = R([a, b]) be the set (actually a vector space) of bounded,
real-valued, Riemann integrable functions on the closed and bounded
interval [a, b], and let X = C([a, b]), be the subset (actually a vector
subspace) of continuous, real-valued functions on [a, b]. For f, g = Y,
define
d(f,g) = sup |f(x) — g(x)|.
x= [a,b]
Does every uniformly Cauchy sequence in R([a, b]) converge uni-
formly to a function in R([a, b])?
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