Parasols in this era were often collapsible as this one is (the hinge is inside the black part of the handle). I love the black lace overlay... oh, I'm inspired to go convert my white modern parasol to something that looks like this!
"Parasols, such as this, reached miniature sizes in the 1850s and 1860s. Coincidentally, the size of hats at this time was also small. This parasol was a frivolity which served no function but acted as an adornment around the head, serving the purpose of a large hat. This piece is special, for fewer parasols from this period exist in museums than from the 1870s onward."