10:33 AA 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,...

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Extracted text: 10:33 AA 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 )