(a) int (int S) = int S
(b) cl (cl S) = cl S
Please write which part of which theorem you have used in each part of your argument.
Directly from the definition of accumulation point show that
(S (upside down U) T)' (is a subset of) S' (upside down U) T'
Find sets S and T for which
(S (upside down U) T)' (is not equal to) S' (upside down U) T'
I have no clue how to do this so im not much help, but I have a definition for you and maybe someone else can figure this out by the definition I give.
Let S is a subset of R. A point x in R is an accumilation point of S if every deleted neighborhood of x contains a point S.