2. Let (X, d) be a metric space and y E X. (i) Prove that the closed ball B[y,2] is a closed set in (X, d). (ii) For X = R, find the open ball B(y, 2) if: (a) d is the usual metric on R; (b) d is the discrete metric on R.

2. Let (X, d) be a metric space and y E X. (i) Prove that the closed ball B[y,2] is a closed set in (X, d). (ii) For X = R, find the open ball B(y, 2) if: (a) d is the usual metric on R; (b) d is the discrete metric on R.

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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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

2. Let (X, d) be a metric space and y E X.
(i) Prove that the closed ball B[y, 2] is a closed set in (X, d).
(ii) For X = R, find the open ball B(y, 2) if:
(a) d is the usual metric on R;
(b) d is the discrete metric on R.

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