State whether the following is true or false: g) The set of integers the usual metric is not compact. h) The set M = { x∈N: x < 7/2 } with the usual metric is connected. i) Suppose metric space X is not path-wise connected then X is not connected.

State whether the following is true or false: g) The set of integers the usual metric is not compact. h) The set M = { x∈N: x < 7/2 } with the usual metric is connected. i) Suppose metric space X is not path-wise connected then X is not connected.

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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Question

3. State whether the following is true or false:

g) The set of integers the usual metric is not compact.

h) The set M = { x∈N: x < 7/2 } with the usual metric is connected.

i) Suppose metric space X is not path-wise connected then X is not connected.

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