Answered: Let (X,dX) and (Y,dY) be metric spaces.… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

Let (X,dX) and (Y,dY) be metric spaces. If the
sequence (fn) of functions from X to Y
converges uniformly to the function f:X→Y,
will the sequence (fn) also converge
pointwise to f?
is it:
Yes, always.
Yes, if the domain is bounded, but not in
general.
Yes, if the functions are bounded, but not in
general.
Yes, if the functions are continuous, but not
in general.
None of the other answers are correct.

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