Let D be a subset of real numbers, and let {fn : D → R} be a sequence of continuous functions that converges uniformly to the function f : D→ R. Show that the function f : D → R is continuous. You need to start with the definition of uniform convergence of a sequence of functions. In the discussion, explain why the uniform convergence is needed.
Let D be a subset of real numbers, and let {fn : D → R} be a sequence of continuous functions that converges uniformly to the function f : D→ R. Show that the function f : D → R is continuous. You need to start with the definition of uniform convergence of a sequence of functions. In the discussion, explain why the uniform convergence is needed.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let D be a subset of real numbers, and let { fn : D → R} be a sequence of continuous functions
that converges uniformly to the function f : D → R. Show that the function f : D → Ris
continuous.
You need to start with the definition of uniform convergence of a sequence of functions. In the
discussion, explain why the uniform convergence is needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf7e432f-d8a7-4405-b581-b444bad9ef3d%2F4da477f5-f091-42be-84a6-290e298d0a82%2Fcwm6kq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let D be a subset of real numbers, and let { fn : D → R} be a sequence of continuous functions
that converges uniformly to the function f : D → R. Show that the function f : D → Ris
continuous.
You need to start with the definition of uniform convergence of a sequence of functions. In the
discussion, explain why the uniform convergence is needed.
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