Shuw that A s open and closed m (K,r) iPf Bd(A) = . %3D

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 4SE: Answer the following questions. 4. Describe how the permutation of ii objects differs from the...
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Question 4 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)
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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