1. Let d, be a metries on X#o and let the function d: X x XR defined by: da, y) 1+ di(1, 9) Vr. y € X. d(r, y) = prove that (X, d) is a metric space, 2. Determine whether the following subsets of R are the neighborhood of of the point 3 A = (1,5), B = {1,2,3, 4,5), N, Z. Q. 3. In R with the usual metric , find: (i) The interior of (2, 3) U (5, 6) (ii) The interior of (5,6) (iii) The limit point of (2,3) (Iv) The closure of the set (1+ n+1 4. Give an example to show that the equality may not hold in An BC An B.

1. Let d, be a metries on X#o and let the function d: X x XR defined by: da, y) 1+ di(1, 9) Vr. y € X. d(r, y) = prove that (X, d) is a metric space, 2. Determine whether the following subsets of R are the neighborhood of of the point 3 A = (1,5), B = {1,2,3, 4,5), N, Z. Q. 3. In R with the usual metric , find: (i) The interior of (2, 3) U (5, 6) (ii) The interior of (5,6) (iii) The limit point of (2,3) (Iv) The closure of the set (1+ n+1 4. Give an example to show that the equality may not hold in An BC An B.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Let A be a non-empty subset of the metric space (X,d). show that a. d(r, A)- d(v. A)l s d(r, y)For all , y E X with d(x, A) = inf{d(x, y) : y € A}
3. Let (Y, p) be of hoxersby f:(Y, d) >CY, P) is example finction a metric space. Give an metric d on Y such that continuous.
Material :Daly analysis
Let (X. d) be a metric space and define p: XxX by ptr.g)= dx.y) Prove that (X,p) is a metric space, (Hint: To prove the triangle inequality, it might help first to show that the function f(t)= is increasing for t≥0.)
Verify that (S, d) is a metric space. 10.2 Prove that d(x, y) < d'(x, y) s2 d(x, y) for all points x, y e R x R, where d is the usual metric and d' is the rectangular metric.
I need the answer as soon as possible
Matreical :Daly analysis
3.5 Show that the metric space (R, d), where d(x, y) = |x – y|, is separable. (4)
Let d: R2 × R2 →R given by xỉ + yỉ + x3 + y½ , if (x1,y1) # (x2, Y2) 0, if (x1, Y1) = (x2, Y2) d((x1.y1).(x2.y2))= { (a) Show that d is a metric. (b) Show that (R2, d) is a complete metric space. (c) Show that (R2, d no a connected metric space