1. Find the interior and boundary of the following sets: a] A- {-:nEN} b] N al 0
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Math 4303 Homework Section 3.4 Topology of R
1. Find the interior and boundary of the following sets:
a] A = { - + : nɛN}
b] N
c] Q
d]
1-4
e) 2 )
SI [0, 1)
2. Classify each set as closed, open, or neither. Justify your answer.
a] A= { - :neN}
b] N
c] Q
d] E). 1-4
e] 가, )
SI [0, 1)
3. Find a counterexample for the following:
a] bd(S UT)= (bds)U (bdT)
b] bd(snT)- (bdS )n (bdT)
4. Let S and T be subsets of R. Prove the following:
a] cl(clS)= clS
b] ct(SUT)- (cIS)U (c!T)
c] cl(snT)C (cIS)n (eIT)
d] Prove/Disprove : c(S nT)- (cIS)n(cIT)
5. Let S and T be subsets of R. Prove the following:
a] int(int S)- int S
b] int(snT)= (int S)n (int 7 )
c] int(SUT)2 (int S)U (int 7)
d] Prove/Disprove : int(S U T)= (int S )U (int 7 )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fb767a74d-9155-4f1f-b483-e3b0be9b5e11%2F29l8tfa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10:33
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A 1-xythos.content.blackboardcdn.com
Math 4303 Homework Section 3.4 Topology of R
1. Find the interior and boundary of the following sets:
a] A = { - + : nɛN}
b] N
c] Q
d]
1-4
e) 2 )
SI [0, 1)
2. Classify each set as closed, open, or neither. Justify your answer.
a] A= { - :neN}
b] N
c] Q
d] E). 1-4
e] 가, )
SI [0, 1)
3. Find a counterexample for the following:
a] bd(S UT)= (bds)U (bdT)
b] bd(snT)- (bdS )n (bdT)
4. Let S and T be subsets of R. Prove the following:
a] cl(clS)= clS
b] ct(SUT)- (cIS)U (c!T)
c] cl(snT)C (cIS)n (eIT)
d] Prove/Disprove : c(S nT)- (cIS)n(cIT)
5. Let S and T be subsets of R. Prove the following:
a] int(int S)- int S
b] int(snT)= (int S)n (int 7 )
c] int(SUT)2 (int S)U (int 7)
d] Prove/Disprove : int(S U T)= (int S )U (int 7 )
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