1. Consider the sets D = { // : n € J}, E = DU{0}. (a) Really quick: complete the definitions - (a) a set E is an open set if... (b) a set E is a closed set if... (c) a set E is a compact set if... (b) For each of D and E decide whether it is closed and whether it is open, and give reason. (c) Find an open cover of D that does not have a finite sub-cover. Prove it. (d) Suppose UE is an open cover of E. Describe precisely how you would determine a finite sub-cover. &EA (e) Using the definition, (a) Is D compact? (b) Is E compact?
1. Consider the sets D = { // : n € J}, E = DU{0}. (a) Really quick: complete the definitions - (a) a set E is an open set if... (b) a set E is a closed set if... (c) a set E is a compact set if... (b) For each of D and E decide whether it is closed and whether it is open, and give reason. (c) Find an open cover of D that does not have a finite sub-cover. Prove it. (d) Suppose UE is an open cover of E. Describe precisely how you would determine a finite sub-cover. &EA (e) Using the definition, (a) Is D compact? (b) Is E compact?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 4CR
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Please do C,D,E only, thanks
![1. Consider the sets D = {: ne J}, E = DU {0}.
(a) Really quick: complete the definitions -
(a) a set E is an open set if...
(b) a set E is a closed set if...
(c) a set E is a compact set if...
(b) For each of D and E decide whether it is closed and whether it is open, and give reason.
(c) Find an open cover of D that does not have a finite sub-cover. Prove it.
(d) Suppose U Ea is an open cover of E. Describe precisely how you would determine a finite sub-cover.
αEA
(e) Using the definition, (a) Is D compact? (b) Is E compact?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597ffd2-5c4b-4c2e-8332-77ce1607dac1%2F65cd8620-c5df-43d4-b23e-c61d2faddf3a%2Foce4fvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the sets D = {: ne J}, E = DU {0}.
(a) Really quick: complete the definitions -
(a) a set E is an open set if...
(b) a set E is a closed set if...
(c) a set E is a compact set if...
(b) For each of D and E decide whether it is closed and whether it is open, and give reason.
(c) Find an open cover of D that does not have a finite sub-cover. Prove it.
(d) Suppose U Ea is an open cover of E. Describe precisely how you would determine a finite sub-cover.
αEA
(e) Using the definition, (a) Is D compact? (b) Is E compact?
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