Q1/Determine âˆ‚A in each case
A=(0,1]in the lower limit topology on R
A={a} in X={a,b,c} with topology {X,âˆ…,{a},{a,b}}
.A={a,c} in X={a,b,c} with topology {X,âˆ…,{a},{a,b}}
A={b} in X={a,b,c} with topology {X,âˆ…,{a},{a,b}}
A=(-1,1)âˆª{2} in the standard topology on R
A=(-1,1)âˆª{2} in the lower limit topology on R
A={(x,0)ÏµR^2 |xÏµR}with the standard topology
A={(x,0)ÏµR^2 |xÏµR} with the vertical interval topology

Q2/for nÏµZ determine âˆ‚({n}) in the digital line topology considering separately the cases where n is even and n is odd. Discuss how your results for âˆ‚({n}) reflect the digital image display structure modeled by the digital line?

Q3/Determine the boundary of each the following subsets of RÂ² in the standard topology
A={(x,x)ÏµR^2 |ÏµR}
A={(x,y)ÏµR^2 |x>0,yâ‰ 0}
A={(1/n,0)ÏµR^2 |n Ïµz_+ }
A={(x,y)ÏµR^2 |0â‰¤x^2-y^2<1}

Q4/Determine âˆ‚([0,1]) in R with the finite complement topology. Justify your result.?

Q5/
a) Give an example to show that the implication A=C-Bâ†’AâˆªB=C fails in general.
b) Show that if BâŠ†C then the implication in (a) holds.

Q6/
a) Show that in general the implication AâˆªB=Câ†’A=c-B fails.
b) Under what condition on A and B in implication in ( a ) is true?

Q7/ Show that âˆ‚A âˆª in A=cl A implies in A=clA-âˆ‚A

Q1/Determine âˆ‚A in each case A=(0,1]in the lower limit topology...