1. Let (S, d) be a discrete metric space and p E S. Identify Sı (p), S1 (p), S2(p). 2. Let R have the usual metric d(x, y) = |x - y|. Sketch S1 (0) and S1(1). 3. Let R have the usual metric d(x, y) = |x - y|. Sketch S1 [0] and S1[1]. 4. Let R? have the usual metric d(x, y) = V(x1 – yı)2 + (x2 – Y2)². Sketch S1 (0, 0), S1(1,1), S1[(0,0)].

1. Let (S, d) be a discrete metric space and p E S. Identify Sı (p), S1 (p), S2(p). 2. Let R have the usual metric d(x, y) = |x - y|. Sketch S1 (0) and S1(1). 3. Let R have the usual metric d(x, y) = |x - y|. Sketch S1 [0] and S1[1]. 4. Let R? have the usual metric d(x, y) = V(x1 – yı)2 + (x2 – Y2)². Sketch S1 (0, 0), S1(1,1), S1[(0,0)].

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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6
Let P(t) be the point on the unit circle U that corresponds to t. If P(t) has the given rectangular coordinates, find(a) P(t + p) , (b) P(t - p) , (c) P(-t ) , (d) P(-t - p)
5. State whether each of the following statements is true or false, in either case substan- tiate/ justify. (b) Let X = {x € R : -1 < x < 0 or 0 < x < 1} with the usual metric. Then X is disconnected.
Please solve number 3
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/Q9. Consider R² with the Euclidean metric. Is (0, 1) = {(x, 0)|0 < x < 1} open, closed, neither, or both? Explain.
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where S = [0, 1]; Q3: (a) In the metric space (S, d), vx, y es. If A = [0,2), then find the following: A; A; A'; JA. d(x,y) = [x - yl: