Topology Q3&4 pls
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
Q3&4 pls
![A is closed
True or False: B is closed
pts True or False: A is a nhood of 0
True or False: B is a nhood of 0
3. Consider the topological space (X, T) where X = R and
T = {X, [0, 1], 0}.
Let A = {1}.
) List all closed sets in (X, T).
Prove cl(A) = R.
s.) Prove int(A) = 0.
4. Let (X, d) be the pseudometric space where X = R and d is the usual
pseudometric. Let A = = {1/n: n=1,2,...}.
Prove that 1 A'.
Prove that 0 € A'.
1
co
the
However, Ho
t
is just
is also e
12. closure
Conside
and ols](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F280016d2-0921-47ae-ade3-8a53295a6a51%2Fisazxpc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A is closed
True or False: B is closed
pts True or False: A is a nhood of 0
True or False: B is a nhood of 0
3. Consider the topological space (X, T) where X = R and
T = {X, [0, 1], 0}.
Let A = {1}.
) List all closed sets in (X, T).
Prove cl(A) = R.
s.) Prove int(A) = 0.
4. Let (X, d) be the pseudometric space where X = R and d is the usual
pseudometric. Let A = = {1/n: n=1,2,...}.
Prove that 1 A'.
Prove that 0 € A'.
1
co
the
However, Ho
t
is just
is also e
12. closure
Conside
and ols
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