State whether the following is true or false: a) The set [0,4] with the usual metric is sequentially compact b) The set [0, 1] with the discrete metric is compact. c) Any cover of a metric space is open.

State whether the following is true or false: a) The set [0,4] with the usual metric is sequentially compact b) The set [0, 1] with the discrete metric is compact. c) Any cover of a metric space is open.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 21E

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Question

State whether the following is true or false:

a) The set [0,4] with the usual metric is sequentially compact

b) The set [0, 1] with the discrete metric is compact.

c) Any cover of a metric space is open.

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