zero!9.J. If F is a non-empty closed set in RP and if x ¢ F, is there a unique pointof F that is nearest to x?9.K. If K is a compact subset of R' and x is a point of Rr, then the set K.{x + y:y € K} is also compact. (This set K,is sometimes called the translationof the set K by r.)9.L. The intersection of two open sets is compact if and only if it is empty.Can the intersection of an infinite collection of open sets be a non-empty com-pact set?%3D

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9.J. If F is a non-empty closed set in R and if x ¢ F, is there a unique point of F that is nearest to x?

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

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zero!
9.J. If F is a non-empty closed set in RP and if x ¢ F, is there a unique point
of F that is nearest to x?
9.K. If K is a compact subset of R' and x is a point of Rr, then the set K.
{x + y:y € K} is also compact. (This set K,is sometimes called the translation
of the set K by r.)
9.L. The intersection of two open sets is compact if and only if it is empty.
Can the intersection of an infinite collection of open sets be a non-empty com-
pact set?
%3D

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