(1) Let X= {1,2.3,4,5. Consider the follouwing topolegy X = {,X, £s}, l,53, 23,53, [ 2,3,s}, ,s3} (a) write down the set of slesed set s in (x,T). (b) Find: 3,43 Int ({2,45), Ext(f2,3,5). (e) If A= E2,3,4} then Pind (the sndiAce topslad).
(1) Let X= {1,2.3,4,5. Consider the follouwing topolegy X = {,X, £s}, l,53, 23,53, [ 2,3,s}, ,s3} (a) write down the set of slesed set s in (x,T). (b) Find: 3,43 Int ({2,45), Ext(f2,3,5). (e) If A= E2,3,4} then Pind (the sndiAce topslad).
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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Question 1 just
![" JO 100
4G
e 12:01
58% O
(O kt X= {1,2,3,4,53. Consider the follewing topolegy o X
= {, X, £s}, ,5}, {23.53, [a,a3,4,5) , {1,s}
(a) write down the set of clesed set s in (X.T).
(b) Find : 3,4,
Int (12,4,5), Ext(£2,3,5).
(c) If A = {2,3,43
, then find T (the subIAce təpaled).
%3D
(2) Let x=R. Then T= {usR; if xeu, then -xeuf
is
a topalesg on R.
dn ofen set in R) which is
an interval and Containing the number -5(thar than K).
(b) is Cl, 8] clased in (R)?(Justifd your anw)
(a) write den
(e)
Find Int (N) where IN is the sel of naturul
nunbers. (justifj your answer)
disprave :
(3) Prove
or
a cluster peil
(a) Fer (X), ACX, if x is
of A, then
cis
beunchry point A.
In (X,2), it xEX, {xy Ee then
ě is
Let (x,7) be
(b)
the
discrete topol oy
(4)
and
ACX.
a topological Space
Shous that A s open and closed n (Kr)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39e9ea01-b453-4a36-9e83-1b5e372e0a88%2Fe7351d16-4766-449f-83ff-5848064dcd0c%2F4kn5jth_processed.jpeg&w=3840&q=75)
Transcribed Image Text:" JO 100
4G
e 12:01
58% O
(O kt X= {1,2,3,4,53. Consider the follewing topolegy o X
= {, X, £s}, ,5}, {23.53, [a,a3,4,5) , {1,s}
(a) write down the set of clesed set s in (X.T).
(b) Find : 3,4,
Int (12,4,5), Ext(£2,3,5).
(c) If A = {2,3,43
, then find T (the subIAce təpaled).
%3D
(2) Let x=R. Then T= {usR; if xeu, then -xeuf
is
a topalesg on R.
dn ofen set in R) which is
an interval and Containing the number -5(thar than K).
(b) is Cl, 8] clased in (R)?(Justifd your anw)
(a) write den
(e)
Find Int (N) where IN is the sel of naturul
nunbers. (justifj your answer)
disprave :
(3) Prove
or
a cluster peil
(a) Fer (X), ACX, if x is
of A, then
cis
beunchry point A.
In (X,2), it xEX, {xy Ee then
ě is
Let (x,7) be
(b)
the
discrete topol oy
(4)
and
ACX.
a topological Space
Shous that A s open and closed n (Kr)
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