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) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

Advanced Engineering Mathematics
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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How do you prove (b)?

Note that the symbol ° represents the interior of a set

Let A and Bdenote subsets of R". (a) Prove that ANBCAN B. Give an example to show that equality does not always hold. (b) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold. (c) Give an example of a function that is C2 but not C³.
Transcribed Image Text:Let A and Bdenote subsets of R". (a) Prove that ANBCAN B. Give an example to show that equality does not always hold. (b) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold. (c) Give an example of a function that is C2 but not C³.
1. There is some magnification beyond which you see only points that belong to S. More precisely, 3e > 0: B(x; e) C S. (1) Def. 4 (Interior) In this case, we say that x belongs to the interior of S. We write Sint for the set of all such points.
Transcribed Image Text:1. There is some magnification beyond which you see only points that belong to S. More precisely, 3e > 0: B(x; e) C S. (1) Def. 4 (Interior) In this case, we say that x belongs to the interior of S. We write Sint for the set of all such points.
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