3. Let (M, d) be a metric space and define D(x, y) = min{1. d(x,y)}, for all r, y € M. Show that (i) D is a metric on M and (ii) D is equivalent to d.
3. Let (M, d) be a metric space and define D(x, y) = min{1. d(x,y)}, for all r, y € M. Show that (i) D is a metric on M and (ii) D is equivalent to d.
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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![3. Let (M, d) be a metric space and define D(x, y) = min{1,d(x,y)},
for all x, y € M. Show that (i) D is a metric on M and (ii) D is
equivalent to d.
4. Let X be the set of all functions from the closed interval [0, 1]
into itself. Show that for any f.g € X,d(f.g) least upperbound
{f(x) - g(x), xe [0, 1]} is a metric.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe23b74-1643-4149-a433-7345e81d4f00%2F88c1cfdb-6f62-453c-8587-73aeb2443bc9%2Fbkxvdjd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let (M, d) be a metric space and define D(x, y) = min{1,d(x,y)},
for all x, y € M. Show that (i) D is a metric on M and (ii) D is
equivalent to d.
4. Let X be the set of all functions from the closed interval [0, 1]
into itself. Show that for any f.g € X,d(f.g) least upperbound
{f(x) - g(x), xe [0, 1]} is a metric.
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