Stir water and salt together in a medium bowl; gradually stir in cornmeal with your fingers until the mixture forms a soft, moist, malleable dough.
Form dough into eight 2-inch diameter balls; pat each ball to flatten into a ⅜-inch-thick arepa patty.
Heat oil in a large skillet over medium heat; fry arepas in batches until golden brown, about 4 to 5 minutes per side.
Transfer cooked arepas to a paper towel-lined plate to drain until cool enough to handle.
Slice halfway through each arepa horizontally with a thin serrated knife to form a pita-like pocket.
