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
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
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
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
