C = containment
int = interior
ext = exterior
cl = closure
Could you please prove if S C T, then
a)int(S) C int(T)
b)ext(T) C ext(S)
c)cl(S) C cl(T)
S C T means S is a subset of T.
(a) for any x in int(S), x is an interior point of S, this means we can find an open set U which contains x and U belongs to S. But S belongs to T. So U also belongs to T. Thus x is an ...
This is a set regarding containment and closure.