Market umbrellas are indeed similar to patio umbrellas except that they come without valances around the circumference.
The Chinese have often been credited for inventing the first to waterproof umbrellas for use as rain protection when they waxed and lacquered their paper parasols after understanding they could protect from the rain as well as the sun. As you hold the pleats in place with your thumb, straighten out the clasp with the other hand, wrap it around the umbrella in the direction of the folded pleats and snap it.