Consider the following statements: (i) If A is not compact then there are infinitely many open covers for A that do not have a finite subcover. (ii) If A is compact there must be an open cover for A that has infinitely many finite subcovers. Which statements are true?

Consider the following statements: (i) If A is not compact then there are infinitely many open covers for A that do not have a finite subcover. (ii) If A is compact there must be an open cover for A that has infinitely many finite subcovers. Which statements are true?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.6: Homomorphisms

Problem 4TFE: Label each of the following statements as either true or false. Every epimorphism is an...

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Question

Consider the following statements:

(i) If A is not compact then there are infinitely many open covers for A that do not have a finite subcover.

(ii) If A is compact there must be an open cover for A that has infinitely many finite subcovers.

Which statements are true?

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