27. Let H be the subspace of the plane described in Example 2.34(c). Let A = {(x,y): 0≤x≤ 1, and 0 ≤ y ≤ 1}. Find the interior and the closure of A in the subspace topology.
27. Let H be the subspace of the plane described in Example 2.34(c). Let A = {(x,y): 0≤x≤ 1, and 0 ≤ y ≤ 1}. Find the interior and the closure of A in the subspace topology.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Topology: Please find examples my professor gave in class as guide to solve question 27
![● DS
ollab.com/collab/ui/session/playback
space
Divine Letter Letter of Recommendation (1).pdf (page 1 of 3)
Good Morning!
Thm 2,29 Suppose (X, T) is a top.
and AEX. Then
T₁ = {UNA:u€T}
top. for A.
is a
A E
Bb
a
Thm 2.30 Suppose (A, TA) is
Subspace of (XT). If B is a base
for T, then a base for TA is
fact
BA={bm AbeB}
PECIS every base el. cont.p meets S
X
6 M
Cor 2.33 the A-derived
set of
SEA is the int. of the T-derived
Set of Swith A
(A)
Def TA is the subspace top. (A,TA) ex (2.34 c) Let X = IR ²
is a subspace of (X, T)
Thm 2.32 if SEA, then
cl₂S = cl(S) ~ A
clx(s)
A
!
16 Share
S ·S, NA
(x)
(+)
(-1,0)
with the usual top.
and let H= {(x, y):y20]. Then (H₂TH).
Let A = [(x,y): 0<x< 1₂ y ²o] ≤H
Claim A is open in the subspace H.
pf Notice A= [(x,y): 0<x< 1}n H₂
rad..
center
So AETH.
Open in (XT) since
{(x,y): 0<x<1}=UC((,y);})
Claim intA=A [Since A is open in H)
claim cl_A = {(x,y): 04x≤1, y>0} ((0,2)=p))
hw S = {(x,y): 0<x<), 0<y<1}
ELIA
p=(-1,0)
CIA
H](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9787c00-cfcc-43da-9235-b2564f9dd12e%2Ff3a65ee1-7ccf-4b28-a6b5-d1eb73808672%2Fx1j4vf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:● DS
ollab.com/collab/ui/session/playback
space
Divine Letter Letter of Recommendation (1).pdf (page 1 of 3)
Good Morning!
Thm 2,29 Suppose (X, T) is a top.
and AEX. Then
T₁ = {UNA:u€T}
top. for A.
is a
A E
Bb
a
Thm 2.30 Suppose (A, TA) is
Subspace of (XT). If B is a base
for T, then a base for TA is
fact
BA={bm AbeB}
PECIS every base el. cont.p meets S
X
6 M
Cor 2.33 the A-derived
set of
SEA is the int. of the T-derived
Set of Swith A
(A)
Def TA is the subspace top. (A,TA) ex (2.34 c) Let X = IR ²
is a subspace of (X, T)
Thm 2.32 if SEA, then
cl₂S = cl(S) ~ A
clx(s)
A
!
16 Share
S ·S, NA
(x)
(+)
(-1,0)
with the usual top.
and let H= {(x, y):y20]. Then (H₂TH).
Let A = [(x,y): 0<x< 1₂ y ²o] ≤H
Claim A is open in the subspace H.
pf Notice A= [(x,y): 0<x< 1}n H₂
rad..
center
So AETH.
Open in (XT) since
{(x,y): 0<x<1}=UC((,y);})
Claim intA=A [Since A is open in H)
claim cl_A = {(x,y): 04x≤1, y>0} ((0,2)=p))
hw S = {(x,y): 0<x<), 0<y<1}
ELIA
p=(-1,0)
CIA
H
Transcribed Image Text:27. Let H be the subspace of the plane described in Example 2.34(c). Let A =
{(x, y): 0 ≤r≤ 1, and 0 ≤ y ≤ 1}. Find the interior and the closure of A
in the subspace topology.
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Is it possible to solve it using words like claim as my professor did in his example in other photo? And also, you didn't find the closure of the subspace (it was part of the question)
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