Let (x, d) be a metric space und ACXnonempty set. Define f:X → R,fix)= inf dex,a).be ashow that:i. R is continuousii x eA if und only if fas= a

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Answered: 4. Let (x, d) be a metric space and ACX…

4. Let (x, d) be a metric space and ACX be nonempty set. Define f:X → IR, fix)= inf dex,a). aE A show that: i. R is continuous i. x eA if nd only if faw=a

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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Question

Let (x, d) be a metric space und ACX
nonempty set. Define f:X → R,
fix)= inf dex,a).
be a
show that:
i. R is continuous
ii x eA if und only if fas= a

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Ques. 1. Let N be a linear space and d be a metric on N such that d(x + z, y + z) = d(x,y), x,y E N and d(ax, ay) = |a|d(x,y), a E F. Show that ||. ||: N - R defined by: Ilx|| = d(x, 0), x E N, is a norm on N. %3D
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