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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?

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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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