Japanese umbrella(?)

Mum's house is full of interesting artefacts from our time living in Hong Kong and taking our holidays around Asia. 

This, she thinks, is a Japanese Umbrella, and the part that protects you from being rained on - what's that called? - seems to be made from oiled paper. 

She tried (in vain) to get me to take it with me today, so I had to give her a brief talk on the positive benefits of keeping clutter around the house. Luckily, I am an expert.