N Hid 4. Let T consist of 0, R, and all intervals of the form (-0, p) for p E R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of X containing P (1) By the definilion of a Topology x, IRE Ţ. along with 'o and x. So J topology on x. is a (2) Let Ui , Uz E T. Let, U,= (-∞, p.) and Uz =(-@,P.), p. , Pa € IR. Let, p= min{ P., P23 also PE IR Now, U, nUz = l-∞, p)E T. (3) Consider any subcollection in T.If sUcBiEl is any subcollection of in T by de finition each Vi contains (-∞, P) where Pi E IR such that iEl. Let, p = maxs P: 3 also PEIR. NOW, Y Vi = (-0, P)E T. e lements %3D %3D LEI what happens if this max doesn't exist? Hence by al, (2), cus p a topology on IR.
N Hid 4. Let T consist of 0, R, and all intervals of the form (-0, p) for p E R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of X containing P (1) By the definilion of a Topology x, IRE Ţ. along with 'o and x. So J topology on x. is a (2) Let Ui , Uz E T. Let, U,= (-∞, p.) and Uz =(-@,P.), p. , Pa € IR. Let, p= min{ P., P23 also PE IR Now, U, nUz = l-∞, p)E T. (3) Consider any subcollection in T.If sUcBiEl is any subcollection of in T by de finition each Vi contains (-∞, P) where Pi E IR such that iEl. Let, p = maxs P: 3 also PEIR. NOW, Y Vi = (-0, P)E T. e lements %3D %3D LEI what happens if this max doesn't exist? Hence by al, (2), cus p a topology on IR.
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
Question
answer the comment
!['N Hid
4. Let T consist of 0, R, and all intervals of the form (-∞, p) for p e R. Prove that T is a
topology on R.
Let X be a set and assume peX Where Iis the collection of all subset of x
containing P along with 'o and x So J is a on x.
(1) By the definilion of a Topology x, IR E Ţ.
topology
(2) Let Ui , Uz E T. Let, U,= (-∞, p,) and Vz =(-», P.), P.,pz € IR. Let, p- min{ P., P23 also PE IR.
Now, U, nUz = (-0∞,p)E T.
%3D
T.If {U,}iEl is any subcollection of elements
(3) Consider any subcollection in
in T by de finition each Vi contains (-o, Pu where Pi E IR such that iel. Let,
P= maxs P. 3 also PEIR. NOW, U vi = (-∞, P)E T.
LEI
what happens if this max doesn't
exist?
Hence by al, l2l, cus mpU
a topology on IR.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93507587-8486-4bd1-9be9-7c1c5dc70b2a%2F6e4cf008-f7b5-41d9-be5c-f528dd77facb%2Fzhm2c7i_processed.png&w=3840&q=75)
Transcribed Image Text:'N Hid
4. Let T consist of 0, R, and all intervals of the form (-∞, p) for p e R. Prove that T is a
topology on R.
Let X be a set and assume peX Where Iis the collection of all subset of x
containing P along with 'o and x So J is a on x.
(1) By the definilion of a Topology x, IR E Ţ.
topology
(2) Let Ui , Uz E T. Let, U,= (-∞, p,) and Vz =(-», P.), P.,pz € IR. Let, p- min{ P., P23 also PE IR.
Now, U, nUz = (-0∞,p)E T.
%3D
T.If {U,}iEl is any subcollection of elements
(3) Consider any subcollection in
in T by de finition each Vi contains (-o, Pu where Pi E IR such that iel. Let,
P= maxs P. 3 also PEIR. NOW, U vi = (-∞, P)E T.
LEI
what happens if this max doesn't
exist?
Hence by al, l2l, cus mpU
a topology on IR.
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.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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)