In any metric space the following three definitions of compactness are equivalent: 1. Every sequence has a
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1. Every sequence has a convergent subsequence.
2. Every open cover has a finite sub cover.
3. Every collection of closed subsets with the finite intersection property has a nonempty intersection.
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1 2 Exercises 1114 and 1115 2 3 Exercise 1116 3 1 Let be a metric space in whic...View the full answer
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