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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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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