Stir water and salt together in a bowl. Gradually stir corn meal into water with your fingers until mixture forms a soft, moist, malleable dough.
Divide dough into 8 golf ball-size balls and pat each one into a patty about 3/8-inch thick.
Heat oil in a skillet over medium heat until shimmering. Working in batches, cook corn patties in hot oil until golden brown, 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 cake horizontally with a thin serrated knife to form a pita-like pocket.
