Theorem 6.2. Let C be a compact subset of Rstd- Then C has a maximum point, that is, there is a point m E C such that for every x E C, x < m.
Theorem 6.2. Let C be a compact subset of Rstd- Then C has a maximum point, that is, there is a point m E C such that for every x E C, x < m.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
100%
How do I show 6.2? Could you explain it in detail?
![{Ca}a€a be a collection of subsets of X.
Cg. The collection C is an open cover
Definition. Let A be a subset of X and let C =
Then C is a cover of A if and only if A U.
of A if and only if C is a cover of A and each C, is open. A subcover c' of a cover C of
A is a subcollection of C whose elements form a cover ofA.
For instance, the open sets {(-n, n)}neN form an open cover of R. A subcover of
this cover is {(-n,n)}n>5, because these sets still cover all of R.
Definition. A space X is compact if and only if every open cover of X has a finite
subcover.
Theorem 6.2. Let C be a compact subset of Rstd. Then C has a maximum point, that is,
there is a point m E C such that for every x E C, x < m.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfa77723-e387-48dc-857e-67a9efe99fb1%2F566cb03a-e536-4d24-9ddf-069628ac3d86%2Fgkdoes_processed.png&w=3840&q=75)
Transcribed Image Text:{Ca}a€a be a collection of subsets of X.
Cg. The collection C is an open cover
Definition. Let A be a subset of X and let C =
Then C is a cover of A if and only if A U.
of A if and only if C is a cover of A and each C, is open. A subcover c' of a cover C of
A is a subcollection of C whose elements form a cover ofA.
For instance, the open sets {(-n, n)}neN form an open cover of R. A subcover of
this cover is {(-n,n)}n>5, because these sets still cover all of R.
Definition. A space X is compact if and only if every open cover of X has a finite
subcover.
Theorem 6.2. Let C be a compact subset of Rstd. Then C has a maximum point, that is,
there is a point m E C such that for every x E C, x < m.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)