3. Do the following task. a. () State formally what do we mean by being a metric space of X with metric d. b. State formally what do we mean by being a complete metric space of X with metric d. c. () Let (X, d) and (X, d) be a metric spaces such that there is NEN satisfying ď (a,b) ≤d(a,b) ≤ ď' (a,b), (va,b € X). Show that if (X, d') is a complete metric space, then (X, d) is also a complete metric space.
3. Do the following task. a. () State formally what do we mean by being a metric space of X with metric d. b. State formally what do we mean by being a complete metric space of X with metric d. c. () Let (X, d) and (X, d) be a metric spaces such that there is NEN satisfying ď (a,b) ≤d(a,b) ≤ ď' (a,b), (va,b € X). Show that if (X, d') is a complete metric space, then (X, d) is also a complete metric space.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:3. Do the following task.
a. () State formally what do we mean by being a metric space of X
with metric d.
b.
State formally what do we mean by being a complete metric
space of X with metric d.
c. () Let (X. d) and (X, d) be a metric spaces such that there is
NEN satisfying
ď (a,b) ≤d(a, b) ≤ d (a,b), (va, b¤X).
Show that if (X, d') is a complete metric space, then (X, d) is also a complete
metric space.
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