MATH 353: Analysis I Exercise 2 2022/21 - : 1. (i) Consider K = {(x, y) R² : -2 < x < 0 and 0

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Math 353 Analysis I Exercise 2 2022 21 1 I Consider K X Y R 2 X 0 And 0 Y 2 Given That A B 1 (179.95 KiB) Viewed 34 times

MATH 353: Analysis I Exercise 2 2022/21 - : 1. (i) Consider K = {(x, y) R² : -2 < x < 0 and 0 <y<2}. Given that (a,b) € K, find the = R2 E number r such that Br((a, b)) CK. (ii) Prove that Br((a,b)) C K where r is defined in (i). (iii) Prove that S - {(x, y) ERP : -2 < x < 0 and 0 Sy <2} is not open. n 2. In each case suppose R” has usual norm. Decide whether the statement is true and give a reason for your answer: (a) In R, 2 € B4(-2) (b) In R, -1.5 € B2(0) (c) In RP,(1.5, 0.5) e B2(-1,0) - 2 2 (d) In R4, (2,0,0, -1) € B3(-1,1,0,1). 2