The function formula_58 defined by formula_59 is continuous, closed, and relatively open, but not (strongly) open. This is because if formula_60 is any open interval in formula_25's domain formula_62 that does contain formula_63 then formula_64 where this open interval is an open subset of both formula_62 and formula_66 However, if formula_60 is any open interval in formula_62 that contains formula_63 then formula_70 which is not an open subset of formula_25's codomain formula_62 but an open subset of formula_73 Because the set of all open intervals in formula_62 is a basis for the Euclidean topology on formula_75 this shows that formula_58 is relatively open but not (strongly) open.