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Which of the following is true? O Finite intersections of compact sets are compact, but there exists an infinite collection of compact sets whose intersection is not compact. O There exists a finite collection of compact sets whose intersection is not compact. O Arbitrary intersections of compact sets are compact, but there exists a finite collection of compact sets whose union is not compact. O Arbitrary intersections of compact sets are compact, and finite unions of compact sets are comapct, but there exists an infinite collection of compact sets whose union is not compact.

Which of the following is true? O Finite intersections of compact sets are compact, but there exists an infinite collection of compact sets whose intersection is not compact. O There exists a finite collection of compact sets whose intersection is not compact. O Arbitrary intersections of compact sets are compact, but there exists a finite collection of compact sets whose union is not compact. O Arbitrary intersections of compact sets are compact, and finite unions of compact sets are comapct, but there exists an infinite collection of compact sets whose union is not compact.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 1TFE: True or False Label each of the following statements as either true or false. Two sets are equal if...
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Which of the following is true? O Finite intersections of compact sets are compact, but there exists an infinite collection of compact sets whose intersection is not compact. O There exists a finite collection of compact sets whose intersection is not compact. O Arbitrary intersections of compact sets are compact, but there exists a finite collection of compact sets whose union is not compact. O Arbitrary intersections of compact sets are compact, and finite unions of compact sets are comapct, but there exists an infinite collection of compact sets whose union is not compact.
Transcribed Image Text:Which of the following is true? O Finite intersections of compact sets are compact, but there exists an infinite collection of compact sets whose intersection is not compact. O There exists a finite collection of compact sets whose intersection is not compact. O Arbitrary intersections of compact sets are compact, but there exists a finite collection of compact sets whose union is not compact. O Arbitrary intersections of compact sets are compact, and finite unions of compact sets are comapct, but there exists an infinite collection of compact sets whose union is not compact.
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