This exercise demonstrates the concepts of boundary point, open and closed sets, etc., highly dependent on X's mother space. Give a reason for its correctness.Suppose Y=[ 0 ,2 ) . In this case A=[1,2 ) is not closed in X; while closed in Y. In addition, G=[0 ,1 )is not open in X while it is open in Y.Suppose X=R^2 and Y=R . In this case A=(0 ,1) is not open in X while it is open in Y. In fact, inside A in X is empty! This exercise demonstrates the concepts of boundary point,open and closed sets, etc., highly dependent on X's motherspace. Give a reason for its correctness.A) Suppose Y = [0,2). In this case Ain X; while closed in Y. In addition, G = [0,1 )is not openin X while it is open in Y.B) Suppose X = R? and Y = R. In this case A = (0,1) is notopen in X while it is open in Y. In fact, inside A in X isempty![1,2 ) is not closed

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Answered: Suppose Y=[ 0 ,2 ) . In this case…

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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This exercise demonstrates the concepts of boundary point, open and closed sets, etc., highly dependent on X's mother space. Give a reason for its correctness.
Suppose Y=[ 0 ,2 ) . In this case A=[1,2 ) is not closed in X; while closed in Y. In addition, G=[0 ,1 )is not open in X while it is open in Y.
Suppose X=R^2 and Y=R . In this case A=(0 ,1) is not open in X while it is open in Y. In fact, inside A in X is empty!

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