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  3. 6. suppose k1 and k2 are compact. why is k1 ∪

6. Suppose K1 and K2 are compact. Why is K1 ∪ K2 necessarily also compact? (a) Write...

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Advance Math

6. Suppose K1 and K2 are compact. Why is K1 ∪ K2 necessarilyalso compact?

(a) Write a proof of this using the sequential definition.

(b) Write a proof of this using the “closed and bounded”definition.

(c) Write a proof of this using open covers and subcovers.

Answer & Explanation Solved by verified expert
3.9 Ratings (443 Votes)
Given K1 K2 are compact set a Let xn be a sequence in K1K2 at leastone of K1 and K2 contains infinite number ofelements of the sequence xn If K1 contains infinite number of points then it hasa covergent subsequence and if K2    See Answer
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