Consider X={a,b,c,d,e} with open sets { },X,{a},{a,b},{a,b.c},{a,b,c,d},{a,c,d}, {c,d}.
a) As given, open sets don't satisfy conditions for the topology. Find two sets should be added to list of open sets to make it topology?
b) in resulting topology space consider set A={a,d,e}. Determine closure of A, interior of A, bd(A), bd(closur of A), bd(interior of A.