The Chinese have a belief that wandering ghosts like to hide in umbrellas as they are afraid of light. They like to hide in dark places.
In the homes of Chinese who are Buddhists and Taoists, there would be altars of deities installed. Some even have charms (yellow paper with incantations) on the main doors. It is believed that ghosts cannot enter such houses unlike they have someone bring them in.. What better way than to hide in umbrellas!
That is why it is not advisable to bring umbrellas into the home after visiting cemeteries, going for wakes for the deceased or other yin places. The action of opening the umbrella would release the ghost into the house.
The umbrella you see above belongs to me. I used it to shield myself from the rain last week and then left it outside the library for a few days. When I wanted to use it yesterday, I opened it and turned it upside down and let it sun for a few minutes first.