the integers. Find the of N. 2. Let X be the set of reals, and let T = {SCX:0€ X-S} U{X}. Show that T is a topology for X and find the closure of the interval A = (1, 2) and of the interval B = (-1,1). 3. Let X be the set of positive integers. For each n E X, let Sn = {k € X:
the integers. Find the of N. 2. Let X be the set of reals, and let T = {SCX:0€ X-S} U{X}. Show that T is a topology for X and find the closure of the interval A = (1, 2) and of the interval B = (-1,1). 3. Let X be the set of positive integers. For each n E X, let Sn = {k € X:
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
Topology
Please follow guide in 2nd photo to solve problem
![Def Let (XT) be a top. space. If SEX,
T-)tmit
then pех на
pt. of Sif
meets S
very
in
a
el. of T cont. p
P
pt. Other than
ex X=IR, T= {0, Ⓡ
Suppole SER and SØ.
Show cI(S)= IR.
Ple+ (pEX=R). The only el. of
is IR and
T cont.
Thm 2.2 let (X₁T) be a top. Space. If SEX
[PECIS) every el. of I cont. p
then
meets S
Thm 23 let (X, TJ be a top. space. If SCX,
Sis T-closed S'ES
then
ef→ Assume (SEX is T-closed) Show S'ES.
Notice S'ES'US = CISS
Assume (S'ES Show S=CIS
"C" SESUSECI (5)
"2" cls=SUSSUS = S
P
IR meets S. By Thm 2.2,
PECI(S). SoX=R)=cl S.
Show c1(S) ≤ X=IR.
CI S=SUS ER UR = IR
Then clS= R
Claim R is closed in (X,T)
ef Since IR SIR and R #ø,
we get cI (IR) = IR ₁
So R is closed.
Claim if SER
is a proper subset
of IR, then S
is NOT closed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F61693be0-361d-497b-a269-1e211cf8722a%2F6eestfw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Def Let (XT) be a top. space. If SEX,
T-)tmit
then pех на
pt. of Sif
meets S
very
in
a
el. of T cont. p
P
pt. Other than
ex X=IR, T= {0, Ⓡ
Suppole SER and SØ.
Show cI(S)= IR.
Ple+ (pEX=R). The only el. of
is IR and
T cont.
Thm 2.2 let (X₁T) be a top. Space. If SEX
[PECIS) every el. of I cont. p
then
meets S
Thm 23 let (X, TJ be a top. space. If SCX,
Sis T-closed S'ES
then
ef→ Assume (SEX is T-closed) Show S'ES.
Notice S'ES'US = CISS
Assume (S'ES Show S=CIS
"C" SESUSECI (5)
"2" cls=SUSSUS = S
P
IR meets S. By Thm 2.2,
PECI(S). SoX=R)=cl S.
Show c1(S) ≤ X=IR.
CI S=SUS ER UR = IR
Then clS= R
Claim R is closed in (X,T)
ef Since IR SIR and R #ø,
we get cI (IR) = IR ₁
So R is closed.
Claim if SER
is a proper subset
of IR, then S
is NOT closed.
![the integers. Find the
of N.
2. Let X be the set of reals, and let T = {SCX:0€ X-S} U{X}. Show
that T is a topology for X and find the closure of the interval A = (1, 2)
and of the interval B = (-1,1).
3. Let X be the set of positive integers. For each n E X, let Sn = {kE X:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F61693be0-361d-497b-a269-1e211cf8722a%2Fl5xvv2vc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:the integers. Find the
of N.
2. Let X be the set of reals, and let T = {SCX:0€ X-S} U{X}. Show
that T is a topology for X and find the closure of the interval A = (1, 2)
and of the interval B = (-1,1).
3. Let X be the set of positive integers. For each n E X, let Sn = {kE X:
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 3 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)