Slice the apple into 1/4" (1/2 cm) pieces and cut slices into quarters.
Scrub the turnips and remove any hairy roots with a vegetable peeler. You don't have to peel the entire root.
Sprinkle salt (2.5% of the weight of the veggies) over the sliced veggies and mix well in a bowl until veggies begin to soften. Some brine will form, but not as much as with cabbage.
Pack mixture into a vessel and weigh down with weight. Cover with an airlock or a clean cloth secured with a rubber band or twist tie.
Ferment 10 to 14 days.
When you like the taste and texture, remove weight, and replace airlock with regular lid. Transfer to the refrigerator.