Any hints or clues appreciated.

Here are my answers so far:

a) if A ∩ S is emtpy then ∅ ∈ ΩS

b) Since A ∈ ΩX(which means A is open), there exists r>0 s.t B(x,r) ⊂ U therfore x ∈ intxA.

c)Don't know

Suppose x ∈ (intxA) ∩ S....

d)?

e)?

f) U is an open set

g) All open sets can be expressed as a union of balls

h) ?