Topology is an element B of B such that z € B and ƒ(B) C C.4. Suppose i: (X.T)(X.S) is the identity function; that is, i(z) = z forevery z E X. Prove that i is continuous if and only if S CT.TY**IV

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Answered: 4. Suppose i: (X.T) (X,S) is the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
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Find the missing coordinate "H" such that quadrilateral EFGH is a rectangle. E(-1,-2) ;F(-3,1) ;G (3,5) **Be sure that the coordinates go in order -- EFGH Show Your Work Find the missing coordinate "H' such that quadrilateral EFGH is a rectangle. E(-1,-2) :F(-3,1) ;G (3,5) I RECOMMEND DRAWING ON PAPER AND UPLOADING A PHOTO of your ANSWER 9. 41 21 -6 -5 -4 -3 -2 -1 1 2 34 56 -2 -3 -4 -5 -61
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4. Suppose i: (X.T) (X,S) is the identity function; that is, i(z) = z for every z E X. Prove that i is continuous if and only if SCT.