namespace latin:/❚

// views
   ClosureSystem ⟶ ClosureOperator: A closed if A fixed point of cl
   ClosureOperator ⟶ ClosureSystem: cl A = intersection of closed supersets of A
   Closeness ↔ ClosureOperator: X close A ⇔ X ‍∈ cl A
   ClosureSystem ⟶ Closeness: A closed if A contains all points close to it 
   Closeness ↔ ClosureSystem: X close A if X in every closed superset of A

for functions f: X ⟶ Y
  f(cl A) ⊆‍ cl f(A)  ⇔  preservation of closeness   ⇔  reflection of closedness  (= continuous)
  f(cl A) ⊇ cl f(A)  ⇔  preservation of closedness
❚

//   views:
      Neighborhood ⟶ Open: NN = supersets of open sets
      Open ⟶ Neighborhood: OO = sets that are neightborhoods for every element
      Open ⟶ Closed: OO = complements of CC
      Closed ⟶ Open: CC = complements of OO
❚